Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000909
(load all 2 compositions to match this statistic)
Mapping
St000909: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 1
([],3)
 => 3
([(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => 2
([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => 2
([],4)
 => 4
([(2,3)],4)
 => 1
([(1,2),(1,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => 3
([(0,2),(0,3),(3,1)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => 1
([(0,3),(3,1),(3,2)],4)
 => 2
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => 1
([],5)
 => 5
([(3,4)],5)
 => 1
([(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(1,4)],5)
 => 3
([(0,1),(0,2),(0,3),(0,4)],5)
 => 4
([(0,2),(0,3),(0,4),(4,1)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 3
([(1,3),(1,4),(4,2)],5)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(2,3),(3,4)],5)
 => 1
([(1,4),(4,2),(4,3)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => 3
([(2,4),(3,4)],5)
 => 2
([(1,4),(2,4),(4,3)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,3)],5)
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
Description
The number of maximal chains of maximal size in a poset.
Matching statistic: St000363
(load all 2 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
St000363: Graphs ⟶ ℤResult quality: 79% ●values known / values provided: 87%●distinct values known / distinct values provided: 79%
Values
([],1)
 => ([],1)
 => 1
([],2)
 => ([(0,1)],2)
 => 2
([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => 2
([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 4
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => 4
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 4
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6
([(2,6),(6,3),(6,4),(6,5)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,6),(2,6),(6,3),(6,4),(6,5)],7)
 => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6
([(2,6),(3,6),(4,6),(6,5)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,6),(2,6),(3,6),(6,4),(6,5)],7)
 => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6
([(0,6),(1,6),(2,6),(3,4),(6,5)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 5
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
 => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ? = 6
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 9
([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
 => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,6),(2,6),(3,4),(3,6),(6,5)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7)
 => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 4
([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
 => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
 => ? = 3
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 10
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 10
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 11
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
 => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
 => ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7)
 => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 3
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7)
 => ? = 5
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7)
 => ([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ? = 4
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
 => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7)
 => ([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ? = 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)
 => ([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7)
 => ([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
Description
The number of minimal vertex covers of a graph. A '''vertex cover''' of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. A vertex cover is minimal if it contains the least possible number of vertices. This is also the leading coefficient of the clique polynomial of the complement of $G$. This is also the number of independent sets of maximal cardinality of $G$.
Matching statistic: St000993
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00251: Graphs —clique sizes⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => [1]
 => ? = 1
([],2)
 => ([(0,1)],2)
 => ([],2)
 => [1,1]
 => 2
([(0,1)],2)
 => ([],2)
 => ([(0,1)],2)
 => [2]
 => 1
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => [1,1,1]
 => 3
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [2,2]
 => 2
([(0,2),(2,1)],3)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => [3]
 => 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [2,2]
 => 2
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => [1,1,1,1]
 => 4
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [2,2,1]
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => 3
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => 2
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [2,2,1]
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => 3
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => 4
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => 1
([],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]
 => 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)
 => [2,1,1,1]
 => 1
([(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)
 => [2,2,1,1]
 => 2
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => 3
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => 4
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => 1
([(0,1),(0,2),(0,3),(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)
 => [3,3,2]
 => 2
([(0,1),(0,2),(0,3),(1,4),(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)
 => [3,3,3]
 => 3
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => 2
([(1,2),(1,3),(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)
 => [3,3,1]
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => 2
([(0,2),(0,3),(2,4),(3,1),(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)
 => [3,3,3]
 => 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => 4
([(2,3),(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)
 => [3,1,1]
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => 3
([(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)
 => [2,2,1,1]
 => 2
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => 4
([(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)
 => [2,2,2,1]
 => 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => 3
([(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)
 => [2,2,2,2]
 => 4
([(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)
 => [2,2,2]
 => 3
([(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)
 => [2,2,2,2]
 => 4
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => 5
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,3]
 => ? = 5
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(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),(3,5),(4,5)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,3,2]
 => ? = 4
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],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)
 => [4,4,4,4]
 => ? = 4
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,3,1]
 => ? = 4
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],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)
 => [4,4,3,3]
 => ? = 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],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)
 => [4,4,4,4]
 => ? = 4
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,3]
 => ? = 5
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(1,2),(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),(3,5),(4,5)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(1,5),(2,5),(5,3),(5,4)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,3,1]
 => ? = 4
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,2),(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),(3,5),(4,5)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
 => ([(1,2),(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),(3,5),(4,5)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,3]
 => ? = 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,2,2,1]
 => ? = 6
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2,2,2]
 => ? = 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => ([(1,2),(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),(3,5),(4,5)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
 => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2,2]
 => ? = 3
([(0,5),(1,5),(4,2),(5,3),(5,4)],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)
 => [4,4,3,3]
 => ? = 2
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,2]
 => ? = 4
([(0,5),(1,5),(4,2),(4,3),(5,4)],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)
 => [4,4,4,4]
 => ? = 4
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(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)],6)
 => [3,3,3,3,2,2]
 => ? = 4
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(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)],6)
 => [2,2,2,2,2,2,2]
 => ? = 7
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(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)],6)
 => [2,2,2,2,2,2,2,2]
 => ? = 8
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],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)
 => [4,4,4,4]
 => ? = 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,1),(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)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,3]
 => ? = 5
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,1),(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)],6)
 => [3,3,3,3,2,2]
 => ? = 4
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,3,1]
 => ? = 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,1),(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)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
 => ([(0,5),(1,4),(2,3)],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)
 => [3,3,3,3,3,3,3,3]
 => ? = 8
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],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)
 => [4,4,4,4]
 => ? = 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],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)
 => [4,4,3,3]
 => ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,3,2]
 => ? = 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2,2]
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,2,2]
 => ? = 7
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => [3,2,2,2,2,2]
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,1),(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)],6)
 => [3,3,2,2,2,2]
 => ? = 2
([(0,5),(1,2),(1,5),(5,3),(5,4)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,2]
 => ? = 4
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2,2,2]
 => ? = 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,3,3,3]
 => ? = 1
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,2]
 => ? = 4
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,2]
 => ? = 4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,2,2,1]
 => ? = 6
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1),(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)],6)
 => [3,3,2,2,2,2]
 => ? = 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
 => ([(0,1),(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)],6)
 => [3,3,3,3,2,2]
 => ? = 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(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),(3,5),(4,5)],6)
 => [3,3,3,3,3,3]
 => ? = 6
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2,2]
 => ? = 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3,3]
 => ? = 5
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,3,3,3]
 => ? = 1
Description
The multiplicity of the largest part of an integer partition.