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Your data matches 135 different statistics following compositions of up to 3 maps.
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(click to perform a complete search on your data)
Matching statistic: St001736
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> 0
([],2)
=> 0
([(0,1)],2)
=> 0
([],3)
=> 0
([(1,2)],3)
=> 0
([(0,2),(1,2)],3)
=> 0
([(0,1),(0,2),(1,2)],3)
=> 1
([],4)
=> 0
([(2,3)],4)
=> 0
([(1,3),(2,3)],4)
=> 0
([(0,3),(1,3),(2,3)],4)
=> 0
([(0,3),(1,2)],4)
=> 0
([(0,3),(1,2),(2,3)],4)
=> 0
([(1,2),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 7
([],5)
=> 0
([(3,4)],5)
=> 0
([(2,4),(3,4)],5)
=> 0
([(1,4),(2,4),(3,4)],5)
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> 0
([(1,4),(2,3)],5)
=> 0
([(1,4),(2,3),(3,4)],5)
=> 0
([(0,1),(2,4),(3,4)],5)
=> 0
([(2,3),(2,4),(3,4)],5)
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> 0
([(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 7
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 7
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 12
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 7
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 13
Description
The total number of cycles in a graph.
For example, the complete graph on four vertices has four triangles and three different four-cycles.
Matching statistic: St001324
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],0)
=> ? = 0
([],2)
=> ([],2)
=> ([(0,1)],2)
=> ([],1)
=> 0
([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ([],0)
=> ? = 0
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 0
([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([],1)
=> 0
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ([],0)
=> ? = 1
([],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 3
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ([],0)
=> ? ∊ {0,1,7}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ([],0)
=> ? ∊ {0,1,7}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ([],0)
=> ? ∊ {0,1,7}
([],5)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(3,4)],5)
=> ([(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 3
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([],0)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([],0)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([],0)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([],0)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([],0)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([],0)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([],0)
=> ? ∊ {1,1,2,3,3,3,6,6,7,7,7,12,13,22,37}
([],6)
=> ([],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(4,5)],6)
=> ([(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(3,5),(4,5)],6)
=> ([(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,4)],6)
=> ([(2,5),(3,4)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,2),(3,5),(4,5)],6)
=> ([(1,2),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,7),(0,8),(0,9),(1,2),(1,3),(1,5),(1,6),(1,9),(2,3),(2,4),(2,6),(2,8),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,7),(1,9),(2,3),(2,5),(2,7),(2,8),(3,4),(3,5),(3,6),(3,8),(4,5),(4,6),(4,9),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,6),(1,7),(1,8),(2,3),(2,5),(2,7),(2,8),(3,4),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,4),(1,8),(1,9),(2,3),(2,4),(2,6),(2,7),(2,9),(3,4),(3,5),(3,7),(3,8),(4,8),(4,9),(5,6),(5,7),(5,8),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,6),(1,7),(1,8),(2,3),(2,5),(2,7),(2,8),(3,4),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(0,7),(0,9),(1,2),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,6),(3,7),(3,9),(4,5),(4,6),(4,8),(4,9),(5,6),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,8),(2,4),(2,5),(2,7),(3,5),(3,6),(3,9),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,7),(0,8),(1,2),(1,4),(1,6),(1,8),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
Description
The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph.
A graph is chordal if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ and $(b,c)$ are edges and $(a,b)$ is not an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
Matching statistic: St001195
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 32%●distinct values known / distinct values provided: 5%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 32%●distinct values known / distinct values provided: 5%
Values
([],1)
=> []
=> []
=> []
=> ? = 0
([],2)
=> []
=> []
=> []
=> ? ∊ {0,0}
([(0,1)],2)
=> [1]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {0,0}
([],3)
=> []
=> []
=> []
=> ? ∊ {0,0}
([(1,2)],3)
=> [1]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {0,0}
([(0,2),(1,2)],3)
=> [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 0
([(0,1),(0,2),(1,2)],3)
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> 1
([],4)
=> []
=> []
=> []
=> ? ∊ {0,0,3,7}
([(2,3)],4)
=> [1]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {0,0,3,7}
([(1,3),(2,3)],4)
=> [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 0
([(0,3),(1,3),(2,3)],4)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(0,3),(1,2)],4)
=> [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 0
([(0,3),(1,2),(2,3)],4)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(1,2),(1,3),(2,3)],4)
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,3,7}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,3,7}
([],5)
=> []
=> []
=> []
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(3,4)],5)
=> [1]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(2,4),(3,4)],5)
=> [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 0
([(1,4),(2,4),(3,4)],5)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(1,4),(2,3)],5)
=> [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 0
([(1,4),(2,3),(3,4)],5)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(0,1),(2,4),(3,4)],5)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(2,3),(2,4),(3,4)],5)
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([],6)
=> []
=> []
=> []
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(4,5)],6)
=> [1]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(3,5),(4,5)],6)
=> [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 0
([(2,5),(3,5),(4,5)],6)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(1,5),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,4)],6)
=> [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 0
([(2,5),(3,4),(4,5)],6)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(1,2),(3,5),(4,5)],6)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(3,4),(3,5),(4,5)],6)
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(0,1),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [7,1]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [9]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> 0
([(1,5),(2,4),(3,4),(3,5)],6)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(0,1),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Matching statistic: St000567
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000567: Integer partitions ⟶ ℤResult quality: 11% ●values known / values provided: 30%●distinct values known / distinct values provided: 11%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000567: Integer partitions ⟶ ℤResult quality: 11% ●values known / values provided: 30%●distinct values known / distinct values provided: 11%
Values
([],1)
=> []
=> ?
=> ? = 0
([],2)
=> []
=> ?
=> ? ∊ {0,0}
([(0,1)],2)
=> [1]
=> []
=> ? ∊ {0,0}
([],3)
=> []
=> ?
=> ? ∊ {0,0,0,1}
([(1,2)],3)
=> [1]
=> []
=> ? ∊ {0,0,0,1}
([(0,2),(1,2)],3)
=> [1,1]
=> [1]
=> ? ∊ {0,0,0,1}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ? ∊ {0,0,0,1}
([],4)
=> []
=> ?
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(2,3)],4)
=> [1]
=> []
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(1,3),(2,3)],4)
=> [1,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(0,3),(1,3),(2,3)],4)
=> [1,1,1]
=> [1,1]
=> 1
([(0,3),(1,2)],4)
=> [1,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(0,3),(1,2),(2,3)],4)
=> [1,1,1]
=> [1,1]
=> 1
([(1,2),(1,3),(2,3)],4)
=> [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [5]
=> []
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [6]
=> []
=> ? ∊ {0,0,0,0,0,0,1,3,7}
([],5)
=> []
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(3,4)],5)
=> [1]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(2,4),(3,4)],5)
=> [1,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(1,4),(2,4),(3,4)],5)
=> [1,1,1]
=> [1,1]
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(1,4),(2,3)],5)
=> [1,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(1,4),(2,3),(3,4)],5)
=> [1,1,1]
=> [1,1]
=> 1
([(0,1),(2,4),(3,4)],5)
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(2,4),(3,4)],5)
=> [3]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(3,4)],5)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [7]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [3]
=> 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [7]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [8]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [7]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [8]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [10]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,1,1,1,2,3,3,6,6,7,7,7,12,13,22,37}
([],6)
=> []
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(4,5)],6)
=> [1]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(3,5),(4,5)],6)
=> [1,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,5),(4,5)],6)
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 6
([(2,5),(3,4)],6)
=> [1,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,4),(4,5)],6)
=> [1,1,1]
=> [1,1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [1,1,1]
=> [1,1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(0,1),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 6
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 3
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4)],6)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 6
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 6
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1,1]
=> [1,1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1,1]
=> [1,1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(0,1),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1]
=> [1,1,1]
=> 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 6
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,1,1]
=> [1,1]
=> 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1]
=> [1,1]
=> 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,3]
=> [3]
=> 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,3,1]
=> [3,1]
=> 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1,1]
=> [1,1]
=> 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 6
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,1,1]
=> [1,1]
=> 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 3
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,3]
=> [3]
=> 0
Description
The sum of the products of all pairs of parts.
This is the evaluation of the second elementary symmetric polynomial which is equal to
$$e_2(\lambda) = \binom{n+1}{2} - \sum_{i=1}^\ell\binom{\lambda_i+1}{2}$$
for a partition $\lambda = (\lambda_1,\dots,\lambda_\ell) \vdash n$, see [1].
This is the maximal number of inversions a permutation with the given shape can have, see [2, cor.2.4].
Matching statistic: St000456
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0
([],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? ∊ {0,0}
([(0,1)],2)
=> ([],2)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {0,0}
([],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? ∊ {0,0,0}
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,2),(1,2)],3)
=> ([],2)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {0,0,0}
([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {0,0,0}
([],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? ∊ {0,0,0,0,0,0,3,7}
([(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],2)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {0,0,0,0,0,0,3,7}
([(0,3),(1,2)],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {0,0,0,0,0,0,3,7}
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {0,0,0,0,0,0,3,7}
([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,3,7}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],2)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {0,0,0,0,0,0,3,7}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {0,0,0,0,0,0,3,7}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {0,0,0,0,0,0,3,7}
([],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,4),(2,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(0,1),(2,4),(3,4)],5)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],2)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(3,4)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,2,3,3,3,6,6,7,7,7,12,13,22,37}
([],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,4)],6)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(1,2),(3,5),(4,5)],6)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St001820
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([],2)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,1)],2)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([],3)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,2),(1,2)],3)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 0 + 1
([],4)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,3),(1,3),(2,3)],4)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,7} + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {0,0,7} + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],3)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,7} + 1
([],5)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(2,4),(3,4)],5)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 2 = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 2 = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],3)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ?
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(3,4)],5)
=> ?
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([],5)
=> ?
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([],5)
=> ?
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],3)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ?
=> ? ∊ {0,0,0,0,0,1,1,1,2,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(2,5),(3,4)],6)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,2),(3,5),(4,5)],6)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 2 = 1 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 2 = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(2,9),(3,8),(4,10),(4,11),(5,7),(5,10),(6,7),(6,11),(7,13),(8,12),(9,12),(10,3),(10,13),(11,2),(11,13),(12,1),(13,8),(13,9)],14)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2 = 1 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 2 = 1 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 0 + 1
([(0,5),(1,4),(2,3)],6)
=> ([],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4)],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(3,5),(4,5)],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4)],6)
=> ?
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 2 = 1 + 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 4 = 3 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 0 + 1
Description
The size of the image of the pop stack sorting operator.
The pop stack sorting operator is defined by $Pop_L^\downarrow(x) = x\wedge\bigwedge\{y\in L\mid y\lessdot x\}$. This statistic returns the size of $Pop_L^\downarrow(L)\}$.
Matching statistic: St001624
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],2)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([],3)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([],4)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,3,7} + 1
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,3,7} + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? ∊ {0,3,7} + 1
([],5)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,25),(2,13),(2,14),(2,15),(2,25),(3,10),(3,11),(3,12),(3,25),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,21),(7,24),(7,29),(8,19),(8,22),(8,29),(9,20),(9,23),(9,29),(10,26),(10,29),(11,27),(11,29),(12,28),(12,29),(13,19),(13,21),(13,26),(14,20),(14,21),(14,27),(15,19),(15,20),(15,28),(16,22),(16,24),(16,26),(17,23),(17,24),(17,27),(18,22),(18,23),(18,28),(19,30),(20,30),(21,30),(22,30),(23,30),(24,30),(25,26),(25,27),(25,28),(26,30),(27,30),(28,30),(29,30)],31)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
=> ? ∊ {0,0,0,1,1,1,2,3,3,3,3,3,6,6,7,7,7,12,13,22,37} + 1
([],6)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,5),(3,4)],6)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,2),(3,5),(4,5)],6)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,29),(2,13),(2,14),(2,15),(2,29),(3,10),(3,11),(3,12),(3,29),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,19),(7,22),(7,25),(7,28),(8,19),(8,20),(8,23),(8,26),(9,19),(9,21),(9,24),(9,27),(10,20),(10,22),(10,30),(11,21),(11,22),(11,31),(12,20),(12,21),(12,32),(13,23),(13,25),(13,30),(14,24),(14,25),(14,31),(15,23),(15,24),(15,32),(16,26),(16,28),(16,30),(17,27),(17,28),(17,31),(18,26),(18,27),(18,32),(19,33),(19,34),(19,35),(20,33),(20,36),(21,33),(21,37),(22,33),(22,38),(23,34),(23,36),(24,34),(24,37),(25,34),(25,38),(26,35),(26,36),(27,35),(27,37),(28,35),(28,38),(29,30),(29,31),(29,32),(30,36),(30,38),(31,37),(31,38),(32,36),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197} + 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
Description
The breadth of a lattice.
The '''breadth''' of a lattice is the least integer $b$ such that any join $x_1\vee x_2\vee\cdots\vee x_n$, with $n > b$, can be expressed as a join over a proper subset of $\{x_1,x_2,\ldots,x_n\}$.
Matching statistic: St000259
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2)],3)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,3)],4)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,3),(2,3)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,3,7}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,3,7}
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,4)],5)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(3,4)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([],6)
=> ([],6)
=> ([],1)
=> ([],1)
=> 0
([(4,5)],6)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,5),(4,5)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,3)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St000260
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2)],3)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,3)],4)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,3),(2,3)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,3,7}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,3,7}
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,4)],5)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(3,4)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3,3,6,6,7,7,7,12,13,22,37}
([],6)
=> ([],6)
=> ([],1)
=> ([],1)
=> 0
([(4,5)],6)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,5),(4,5)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,3)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000302
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2)],3)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,3)],4)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,3),(2,3)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,3,7}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,3,7}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,3,7}
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,4)],5)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(3,4)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 6
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,6,7,7,7,12,13,22,37}
([],6)
=> ([],6)
=> ([],1)
=> ([],1)
=> 0
([(4,5)],6)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,5),(4,5)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,3)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,10,10,10,10,11,12,12,12,12,12,12,12,12,12,13,13,13,13,13,14,15,18,18,19,19,20,21,21,22,22,22,22,22,22,23,24,30,32,33,35,36,37,37,37,38,39,52,53,54,59,63,85,91,133,197}
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 6
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 6
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 6
Description
The determinant of the distance matrix of a connected graph.
The following 125 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001651The Frankl number of a lattice. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000929The constant term of the character polynomial of an integer partition. St000934The 2-degree of an integer partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001128The exponens consonantiae of a partition. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000442The maximal area to the right of an up step of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000478Another weight of a partition according to Alladi. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000658The number of rises of length 2 of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000693The modular (standard) major index of a standard tableau. St000735The last entry on the main diagonal of a standard tableau. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000874The position of the last double rise in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000946The sum of the skew hook positions in a Dyck path. St000947The major index east count of a Dyck path. St000976The sum of the positions of double up-steps of a Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001139The number of occurrences of hills of size 2 in a Dyck path. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001845The number of join irreducibles minus the rank of a lattice. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001626The number of maximal proper sublattices of a lattice. St000264The girth of a graph, which is not a tree. St001060The distinguishing index of a graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001498The normalised height of a Nakayama algebra with magnitude 1. St001570The minimal number of edges to add to make a graph Hamiltonian. St000455The second largest eigenvalue of a graph if it is integral. St001396Number of triples of incomparable elements in a finite poset. St001964The interval resolution global dimension of a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000137The Grundy value of an integer partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000944The 3-degree of an integer partition. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001175The size of a partition minus the hook length of the base cell. St001176The size of a partition minus its first part. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001279The sum of the parts of an integer partition that are at least two. St001280The number of parts of an integer partition that are at least two. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001383The BG-rank of an integer partition. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001389The number of partitions of the same length below the given integer partition. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001432The order dimension of the partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001525The number of symmetric hooks on the diagonal of a partition. St001527The cyclic permutation representation number of an integer partition. St001541The Gini index of an integer partition. St001571The Cartan determinant of the integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001587Half of the largest even part of an integer partition. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001657The number of twos in an integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001961The sum of the greatest common divisors of all pairs of parts. St000273The domination number of a graph. St000544The cop number of a graph. St001829The common independence number of a graph.
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