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Your data matches 110 different statistics following compositions of up to 3 maps.
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(click to perform a complete search on your data)
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)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([],4)
=> ([],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)
=> 1
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],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),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
([(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),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([],5)
=> ([],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)
=> 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 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)
=> ([(0,4),(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)
=> 1
([],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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,2),(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)
=> 2
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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),(0,2),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,2),(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)
=> 2
([(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)
=> ([(0,1),(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)
=> 1
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St001512
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([],4)
=> ([],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)
=> 1
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],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),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
([(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),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([],5)
=> ([],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)
=> 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 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)
=> ([(0,4),(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)
=> 1
([],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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,2),(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)
=> 2
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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),(0,2),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,1),(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)
=> 1
([(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)
=> ([(0,2),(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)
=> 2
([(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)
=> ([(0,1),(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)
=> 1
Description
The minimum rank of a graph.
The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices whose entry in row $i$ and column $j$ (for $i\neq j$) is nonzero whenever $\{i, j\}$ is an edge in
$G$, and zero otherwise.
Matching statistic: St001093
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],2)
=> ([],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 1 + 1
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2 = 1 + 1
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2 = 1 + 1
([],4)
=> ([],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)
=> 2 = 1 + 1
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([],5)
=> ([],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)
=> 2 = 1 + 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 2 + 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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(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)
=> ([(0,4),(1,3),(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)
=> 3 = 2 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 2 + 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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 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)
=> ([(0,4),(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)
=> 2 = 1 + 1
([],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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(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)
=> 3 = 2 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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),(0,2),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 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)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],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)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(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)
=> 3 = 2 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
Description
The detour number of a graph.
This is the number of vertices in a longest induced path in a graph.
Note that [1] defines the detour number as the number of edges in a longest induced path, which is unsuitable for the empty graph.
Matching statistic: St001674
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],2)
=> ([],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 1 + 1
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2 = 1 + 1
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2 = 1 + 1
([],4)
=> ([],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)
=> 2 = 1 + 1
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([],5)
=> ([],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)
=> 2 = 1 + 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 2 + 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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(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)
=> ([(0,4),(1,3),(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)
=> 3 = 2 + 1
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 2 + 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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 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)
=> ([(0,4),(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)
=> 2 = 1 + 1
([],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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(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)
=> 3 = 2 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
([(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),(0,2),(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)
=> 2 = 1 + 1
([(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)
=> ([(0,1),(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)
=> 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)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],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)
=> 2 = 1 + 1
([(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)
=> ([(0,2),(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)
=> 3 = 2 + 1
([(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)
=> ([(0,1),(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)
=> 2 = 1 + 1
Description
The number of vertices of the largest induced star graph in the graph.
Matching statistic: St000455
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0 - 2
([],2)
=> ([],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> -1 = 1 - 2
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> -1 = 1 - 2
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> -1 = 1 - 2
([],4)
=> ([],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)
=> -1 = 1 - 2
([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> -1 = 1 - 2
([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> -1 = 1 - 2
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> -1 = 1 - 2
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0 = 2 - 2
([(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),(0,3),(1,2),(1,3),(2,3)],4)
=> -1 = 1 - 2
([],5)
=> ([],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)
=> -1 = 1 - 2
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -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)
=> ([(0,4),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> -1 = 1 - 2
([],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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,2),(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 = 2 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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),(0,2),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,2),(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 = 2 - 2
([(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)
=> ([(0,1),(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)
=> -1 = 1 - 2
([(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)
=> ([(0,2),(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 = 2 - 2
([(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)
=> ([(0,3),(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)
=> ? = 2 - 2
([(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)
=> ([(0,3),(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)
=> ? = 2 - 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
=> ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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)
=> ? = 2 - 2
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Matching statistic: St000260
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 67%
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 67%
Values
([],1)
=> [1] => [1] => ([],1)
=> 0
([],2)
=> [2] => [1,1] => ([(0,1)],2)
=> 1
([],3)
=> [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,2)],3)
=> [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
([],4)
=> [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(2,3)],4)
=> [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(1,3),(2,3)],4)
=> [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2)],4)
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2),(2,3)],4)
=> [1,1,1,1] => [4] => ([],4)
=> ? = 2
([(1,2),(1,3),(2,3)],4)
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([],5)
=> [5] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(3,4)],5)
=> [1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(2,4),(3,4)],5)
=> [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,4),(2,4),(3,4)],5)
=> [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,4),(2,3)],5)
=> [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,4),(2,3),(3,4)],5)
=> [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(0,1),(2,4),(3,4)],5)
=> [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(2,3),(2,4),(3,4)],5)
=> [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [1,1,1,1,1] => [5] => ([],5)
=> ? = 2
([(1,4),(2,3),(2,4),(3,4)],5)
=> [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [1,1,1,1,1] => [5] => ([],5)
=> ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [1,1,1,1,1] => [5] => ([],5)
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [1,1,1,1,1] => [5] => ([],5)
=> ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([],6)
=> [6] => [1,1,1,1,1,1] => ([(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)
=> 1
([(4,5)],6)
=> [1,5] => [2,1,1,1,1] => ([(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)
=> 1
([(3,5),(4,5)],6)
=> [1,1,4] => [3,1,1,1] => ([(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)
=> 1
([(2,5),(3,5),(4,5)],6)
=> [1,2,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [1,3,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(2,5),(3,4)],6)
=> [2,4] => [1,2,1,1,1] => ([(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)
=> 1
([(2,5),(3,4),(4,5)],6)
=> [1,1,1,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,2),(3,5),(4,5)],6)
=> [1,1,1,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(3,4),(3,5),(4,5)],6)
=> [2,4] => [1,2,1,1,1] => ([(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)
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [1,1,2,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,2,1,1] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [1,2,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,1,3] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [1,1,2,1,1] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [1,1,2,1,1] => ([(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)
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [1,2,1,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [2,1,3] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [1,2,1,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [2,1,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [1,1,2,1,1] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [1,2,1,1,1] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [1,2,1,1,1] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [1,2,1,1,1] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [1,2,2,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [1,2,1,1,1] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> [1,3,1,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,1,1,1] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [1,1,3,1,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,1,1,1,1,1] => [7] => ([],7)
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,1,1,1,1,1] => [7] => ([],7)
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,2,1,1,1] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,2,1,1,1] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ? = 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> [1,1,1,1,1,1,1] => [7] => ([],7)
=> ? = 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 1
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> [1,1,1,2,1,1] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000781
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> []
=> ? = 0
([],2)
=> [1,1]
=> [1]
=> 1
([],3)
=> [1,1,1]
=> [1,1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> 1
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 2
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ? = 2
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [3,3]
=> [3]
=> 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [4,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ? = 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> [7]
=> []
=> ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 1
Description
The number of proper colouring schemes of a Ferrers diagram.
A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1].
This statistic is the number of distinct such integer partitions that occur.
Matching statistic: St001901
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> []
=> ? = 0
([],2)
=> [1,1]
=> [1]
=> 1
([],3)
=> [1,1,1]
=> [1,1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> 1
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 2
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ? = 2
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [3,3]
=> [3]
=> 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [4,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ? = 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> [7]
=> []
=> ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ? = 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> ? = 1
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Matching statistic: St000183
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
St000183: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
St000183: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 0
([],2)
=> [1,1]
=> [1]
=> [1]
=> 1
([],3)
=> [1,1,1]
=> [1,1]
=> [1,1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> [1]
=> 1
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1,1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> [1]
=> 1
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> [2]
=> 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 2
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> [1]
=> 1
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1,1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> [1]
=> 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [3]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> [1]
=> 1
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> [2]
=> 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1,1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> [1]
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> [1]
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> [1]
=> 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> [2]
=> 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> [1]
=> 1
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [3,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1,1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [3]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> [2]
=> 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [3,3]
=> [3]
=> [2,1]
=> 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [4]
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [4,2]
=> [2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [3]
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> [2]
=> 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> [1]
=> 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> ?
=> ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> ?
=> ? = 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> ?
=> ? = 1
Description
The side length of the Durfee square of an integer partition.
Given a partition $\lambda = (\lambda_1,\ldots,\lambda_n)$, the Durfee square is the largest partition $(s^s)$ whose diagram fits inside the diagram of $\lambda$. In symbols, $s = \max\{ i \mid \lambda_i \geq i \}$.
This is also known as the Frobenius rank.
Matching statistic: St000326
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000326: Binary words ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000326: Binary words ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> []
=> => ? = 0
([],2)
=> [1,1]
=> [1]
=> 10 => 1
([],3)
=> [1,1,1]
=> [1,1]
=> 110 => 1
([(1,2)],3)
=> [2,1]
=> [1]
=> 10 => 1
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> 1110 => 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> 110 => 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 10 => 1
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 100 => 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> => ? = 2
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 10 => 1
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 11110 => 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 1110 => 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 110 => 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 10 => 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1010 => 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 10 => 1
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 100 => 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> 110 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> => ? = 2
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 10 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> 10 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 10 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 100 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 10 => 1
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 111110 => 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> 11110 => 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1110 => 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 110 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> 10110 => 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 110 => 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1010 => 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> 1110 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 100 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 110 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> 110 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [3,3]
=> [3]
=> 1000 => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> 110 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> 1100 => 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [4,2]
=> [2]
=> 100 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1010 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 100 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> 10 => 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> => ? = 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> [7]
=> []
=> => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> => ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> [7]
=> []
=> => ? = 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [7]
=> []
=> => ? = 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> [7]
=> []
=> => ? = 1
Description
The position of the first one in a binary word after appending a 1 at the end.
Regarding the binary word as a subset of $\{1,\dots,n,n+1\}$ that contains $n+1$, this is the minimal element of the set.
The following 100 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000847The number of standard Young tableaux whose descent set is the binary word. St000913The number of ways to refine the partition into singletons. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001196The global dimension of $A$ minus the global dimension of $eAe$ for the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001256Number of simple reflexive modules that are 2-stable reflexive. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001722The number of minimal chains with small intervals between a binary word and the top element. 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. St000290The major index of a binary word. St000291The number of descents of a binary word. St000293The number of inversions of a binary word. St000296The length of the symmetric border of a binary word. St000347The inversion sum of a binary word. St000629The defect of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000921The number of internal inversions of a binary word. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St001025Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001175The size of a partition minus the hook length of the base cell. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001371The length of the longest Yamanouchi prefix of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001471The magnitude of a Dyck path. St001485The modular major index of a binary word. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St000699The toughness times the least common multiple of 1,. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St000299The number of nonisomorphic vertex-induced subtrees. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St000456The monochromatic index of a connected graph. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000618The number of self-evacuating tableaux of given shape. St001432The order dimension of the partition. St001592The maximal number of simple paths between any two different vertices of a graph. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. 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. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000225Difference between largest and smallest parts in a partition. St000379The number of Hamiltonian cycles in a graph. 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. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St000929The constant term of the character polynomial of an integer partition. St000944The 3-degree of an integer partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St000264The girth of a graph, which is not a tree. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000284The Plancherel distribution on integer partitions. 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. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St001877Number of indecomposable injective modules with projective dimension 2. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. 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. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001875The number of simple modules with projective dimension at most 1.
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