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Your data matches 45 different statistics following compositions of up to 3 maps.
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Matching statistic: St000259
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(load all 4 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([(0,1)],2)
=> 1
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([],4)
=> ([],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)
=> 2
([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 3
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 2
([],5)
=> ([],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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 3
([(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)
=> 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 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)
=> 3
([(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)
=> 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)
=> 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)
=> 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
([(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)
=> 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 3
([],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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 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)
=> 3
([(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)
=> 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 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)
=> 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 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)
=> 2
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St000455
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0 - 2
([],2)
=> ([],2)
=> ([],2)
=> ([(0,1)],2)
=> -1 = 1 - 2
([],3)
=> ([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> -1 = 1 - 2
([(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 2 - 2
([],4)
=> ([],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> -1 = 1 - 2
([(2,3)],4)
=> ([(2,3)],4)
=> ([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0 = 2 - 2
([(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 2 - 2
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0 = 2 - 2
([(0,3),(1,2),(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)
=> ([],4)
=> ? = 3 - 2
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 2 - 2
([],5)
=> ([],5)
=> ([],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)
=> ([(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
([(2,4),(3,4)],5)
=> ([(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 = 2 - 2
([(1,4),(2,4),(3,4)],5)
=> ([(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 = 2 - 2
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
([(1,4),(2,3),(3,4)],5)
=> ([(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 = 2 - 2
([(0,1),(2,4),(3,4)],5)
=> ([(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 = 2 - 2
([(2,3),(2,4),(3,4)],5)
=> ([(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 = 2 - 2
([(0,4),(1,4),(2,3),(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)
=> ([],5)
=> ? = 3 - 2
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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 = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(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 = 2 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 3 - 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)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 3 - 2
([(0,4),(1,3),(2,3),(2,4)],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)
=> ([],5)
=> ? = 2 - 2
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(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 = 2 - 2
([(0,3),(1,2),(1,4),(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)
=> ([],5)
=> ? = 3 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 2 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 4 - 2
([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 3 - 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)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 3 - 2
([],6)
=> ([],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)
=> -1 = 1 - 2
([(4,5)],6)
=> ([(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 = 2 - 2
([(3,5),(4,5)],6)
=> ([(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 = 2 - 2
([(2,5),(3,5),(4,5)],6)
=> ([(2,3),(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 = 2 - 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(2,5),(3,4)],6)
=> ([(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 = 2 - 2
([(2,5),(3,4),(4,5)],6)
=> ([(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 = 2 - 2
([(1,2),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(3,4),(3,5),(4,5)],6)
=> ([(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 = 2 - 2
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 0 = 2 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(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 = 2 - 2
([(0,5),(1,5),(2,5),(3,4),(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)
=> ([],6)
=> ? = 3 - 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,3),(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 = 2 - 2
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(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)
=> ([],6)
=> ? = 2 - 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)
=> ([(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 = 2 - 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,5),(2,3),(2,4),(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)
=> ([(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)
=> ([],6)
=> ? = 3 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,5),(1,5),(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)
=> ([(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)
=> ([],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],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)
=> ([],6)
=> ? = 2 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],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)
=> ([],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,5),(1,4),(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)
=> ([(0,1),(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 0 = 2 - 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 0 = 2 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,5),(1,4),(2,3),(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)
=> ([],6)
=> ? = 2 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 0 = 2 - 2
([(0,4),(1,5),(2,3),(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)
=> ([],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(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)
=> ([],6)
=> ? = 2 - 2
([(0,5),(1,4),(2,3),(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)
=> ([],6)
=> ? = 2 - 2
([(0,5),(1,2),(1,5),(2,4),(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)
=> ([(0,1),(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,3),(2,4),(2,5),(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)
=> ([(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(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)
=> ([],6)
=> ? = 2 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(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)
=> ([],6)
=> ? = 2 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(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)
=> ([],6)
=> ? = 2 - 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(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)
=> ([],6)
=> ? = 2 - 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(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)
=> ([],6)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(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)
=> ([],6)
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(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)
=> ([],6)
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(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)
=> ([(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)
=> ([],6)
=> ? = 3 - 2
([(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)
=> ([(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)
=> ([],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(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)
=> ([(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)
=> ([],6)
=> ? = 2 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(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)
=> ([(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)
=> ([],6)
=> ? = 4 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(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)
=> ([(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(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)
=> ([(0,1),(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)
=> ([],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(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)
=> ([(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)
=> ([],6)
=> ? = 4 - 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(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)
=> ([(0,1),(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(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)
=> ([(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(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)
=> ([(0,1),(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)
=> ([],6)
=> ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(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)],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)
=> ([],6)
=> ? = 2 - 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(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)
=> ([],6)
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(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)
=> ([(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)
=> ([],6)
=> ? = 2 - 2
([(0,1),(0,2),(1,5),(2,4),(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)
=> ([(0,1),(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)
=> ([],6)
=> ? = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],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)
=> ([],6)
=> ? = 2 - 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],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)
=> ([],6)
=> ? = 3 - 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: St000781
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 25%●distinct values known / distinct values provided: 14%
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 25%●distinct values known / distinct values provided: 14%
Values
([],1)
=> ([],1)
=> [1]
=> []
=> ? = 0 - 1
([],2)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([],3)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(1,2)],3)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([],4)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(2,3)],4)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([],5)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(3,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 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)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([],6)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,5),(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4)],6)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 4 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 4 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ? = 2 - 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 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 25%●distinct values known / distinct values provided: 14%
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 25%●distinct values known / distinct values provided: 14%
Values
([],1)
=> ([],1)
=> [1]
=> []
=> ? = 0 - 1
([],2)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([],3)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(1,2)],3)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([],4)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(2,3)],4)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([],5)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(3,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 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)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([],6)
=> ([],1)
=> [1]
=> []
=> ? = 1 - 1
([(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,5),(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4)],6)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 4 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 4 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? = 3 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [6]
=> []
=> ? = 2 - 1
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Matching statistic: St000618
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000618: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000618: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Values
([],1)
=> []
=> ?
=> ? = 0 - 1
([],2)
=> []
=> ?
=> ? = 1 - 1
([],3)
=> []
=> ?
=> ? = 1 - 1
([(1,2)],3)
=> [1]
=> []
=> ? = 2 - 1
([],4)
=> []
=> ?
=> ? = 1 - 1
([(2,3)],4)
=> [1]
=> []
=> ? = 2 - 1
([(1,3),(2,3)],4)
=> [2]
=> []
=> ? = 2 - 1
([(0,3),(1,2)],4)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> [3]
=> []
=> ? = 2 - 1
([],5)
=> []
=> ?
=> ? = 1 - 1
([(3,4)],5)
=> [1]
=> []
=> ? = 2 - 1
([(2,4),(3,4)],5)
=> [2]
=> []
=> ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(1,4),(2,3)],5)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> []
=> ? = 3 - 1
([],6)
=> []
=> ?
=> ? = 1 - 1
([(4,5)],6)
=> [1]
=> []
=> ? = 2 - 1
([(3,5),(4,5)],6)
=> [2]
=> []
=> ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(2,5),(3,4)],6)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(3,6),(4,5)],7)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [2,1,1]
=> [1,1]
=> 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
=> [5,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
Description
The number of self-evacuating tableaux of given shape.
This is the same as the number of standard domino tableaux of the given shape.
Matching statistic: St001432
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001432: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001432: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Values
([],1)
=> []
=> ?
=> ? = 0 - 1
([],2)
=> []
=> ?
=> ? = 1 - 1
([],3)
=> []
=> ?
=> ? = 1 - 1
([(1,2)],3)
=> [1]
=> []
=> ? = 2 - 1
([],4)
=> []
=> ?
=> ? = 1 - 1
([(2,3)],4)
=> [1]
=> []
=> ? = 2 - 1
([(1,3),(2,3)],4)
=> [2]
=> []
=> ? = 2 - 1
([(0,3),(1,2)],4)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> [3]
=> []
=> ? = 2 - 1
([],5)
=> []
=> ?
=> ? = 1 - 1
([(3,4)],5)
=> [1]
=> []
=> ? = 2 - 1
([(2,4),(3,4)],5)
=> [2]
=> []
=> ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(1,4),(2,3)],5)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> []
=> ? = 3 - 1
([],6)
=> []
=> ?
=> ? = 1 - 1
([(4,5)],6)
=> [1]
=> []
=> ? = 2 - 1
([(3,5),(4,5)],6)
=> [2]
=> []
=> ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(2,5),(3,4)],6)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(3,6),(4,5)],7)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [2,1,1]
=> [1,1]
=> 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
=> [5,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
Description
The order dimension of the partition.
Given a partition $\lambda$, let $I(\lambda)$ be the principal order ideal in the Young lattice generated by $\lambda$. The order dimension of a partition is defined as the order dimension of the poset $I(\lambda)$.
Matching statistic: St001609
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001609: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001609: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Values
([],1)
=> []
=> ?
=> ? = 0 - 1
([],2)
=> []
=> ?
=> ? = 1 - 1
([],3)
=> []
=> ?
=> ? = 1 - 1
([(1,2)],3)
=> [1]
=> []
=> ? = 2 - 1
([],4)
=> []
=> ?
=> ? = 1 - 1
([(2,3)],4)
=> [1]
=> []
=> ? = 2 - 1
([(1,3),(2,3)],4)
=> [2]
=> []
=> ? = 2 - 1
([(0,3),(1,2)],4)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> [3]
=> []
=> ? = 2 - 1
([],5)
=> []
=> ?
=> ? = 1 - 1
([(3,4)],5)
=> [1]
=> []
=> ? = 2 - 1
([(2,4),(3,4)],5)
=> [2]
=> []
=> ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(1,4),(2,3)],5)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> []
=> ? = 3 - 1
([],6)
=> []
=> ?
=> ? = 1 - 1
([(4,5)],6)
=> [1]
=> []
=> ? = 2 - 1
([(3,5),(4,5)],6)
=> [2]
=> []
=> ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(2,5),(3,4)],6)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(3,6),(4,5)],7)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [2,1,1]
=> [1,1]
=> 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
=> [5,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
Description
The number of coloured trees such that the multiplicities of colours are given by a partition.
In particular, the value on the partition $(n)$ is the number of unlabelled trees on $n$ vertices, [[oeis:A000055]], whereas the value on the partition $(1^n)$ is the number of labelled trees [[oeis:A000272]].
Matching statistic: St001780
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001780: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001780: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Values
([],1)
=> []
=> ?
=> ? = 0 - 1
([],2)
=> []
=> ?
=> ? = 1 - 1
([],3)
=> []
=> ?
=> ? = 1 - 1
([(1,2)],3)
=> [1]
=> []
=> ? = 2 - 1
([],4)
=> []
=> ?
=> ? = 1 - 1
([(2,3)],4)
=> [1]
=> []
=> ? = 2 - 1
([(1,3),(2,3)],4)
=> [2]
=> []
=> ? = 2 - 1
([(0,3),(1,2)],4)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> [3]
=> []
=> ? = 2 - 1
([],5)
=> []
=> ?
=> ? = 1 - 1
([(3,4)],5)
=> [1]
=> []
=> ? = 2 - 1
([(2,4),(3,4)],5)
=> [2]
=> []
=> ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(1,4),(2,3)],5)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> []
=> ? = 3 - 1
([],6)
=> []
=> ?
=> ? = 1 - 1
([(4,5)],6)
=> [1]
=> []
=> ? = 2 - 1
([(3,5),(4,5)],6)
=> [2]
=> []
=> ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(2,5),(3,4)],6)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(3,6),(4,5)],7)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [2,1,1]
=> [1,1]
=> 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
=> [5,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
Description
The order of promotion on the set of standard tableaux of given shape.
Matching statistic: St001899
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001899: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001899: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Values
([],1)
=> []
=> ?
=> ? = 0 - 1
([],2)
=> []
=> ?
=> ? = 1 - 1
([],3)
=> []
=> ?
=> ? = 1 - 1
([(1,2)],3)
=> [1]
=> []
=> ? = 2 - 1
([],4)
=> []
=> ?
=> ? = 1 - 1
([(2,3)],4)
=> [1]
=> []
=> ? = 2 - 1
([(1,3),(2,3)],4)
=> [2]
=> []
=> ? = 2 - 1
([(0,3),(1,2)],4)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> [3]
=> []
=> ? = 2 - 1
([],5)
=> []
=> ?
=> ? = 1 - 1
([(3,4)],5)
=> [1]
=> []
=> ? = 2 - 1
([(2,4),(3,4)],5)
=> [2]
=> []
=> ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(1,4),(2,3)],5)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> []
=> ? = 3 - 1
([],6)
=> []
=> ?
=> ? = 1 - 1
([(4,5)],6)
=> [1]
=> []
=> ? = 2 - 1
([(3,5),(4,5)],6)
=> [2]
=> []
=> ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(2,5),(3,4)],6)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(3,6),(4,5)],7)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [2,1,1]
=> [1,1]
=> 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
=> [5,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
Description
The total number of irreducible representations contained in the higher Lie character for an integer partition.
Matching statistic: St001900
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001900: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001900: Integer partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Values
([],1)
=> []
=> ?
=> ? = 0 - 1
([],2)
=> []
=> ?
=> ? = 1 - 1
([],3)
=> []
=> ?
=> ? = 1 - 1
([(1,2)],3)
=> [1]
=> []
=> ? = 2 - 1
([],4)
=> []
=> ?
=> ? = 1 - 1
([(2,3)],4)
=> [1]
=> []
=> ? = 2 - 1
([(1,3),(2,3)],4)
=> [2]
=> []
=> ? = 2 - 1
([(0,3),(1,2)],4)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> [3]
=> []
=> ? = 2 - 1
([],5)
=> []
=> ?
=> ? = 1 - 1
([(3,4)],5)
=> [1]
=> []
=> ? = 2 - 1
([(2,4),(3,4)],5)
=> [2]
=> []
=> ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(1,4),(2,3)],5)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
=> [3]
=> []
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4]
=> []
=> ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [6]
=> []
=> ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [9]
=> []
=> ? = 3 - 1
([],6)
=> []
=> ?
=> ? = 1 - 1
([(4,5)],6)
=> [1]
=> []
=> ? = 2 - 1
([(3,5),(4,5)],6)
=> [2]
=> []
=> ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(2,5),(3,4)],6)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
=> [3]
=> []
=> ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [5]
=> []
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ? = 3 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [6]
=> []
=> ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(3,6),(4,5)],7)
=> [1,1]
=> [1]
=> 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
=> [2,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [2,2]
=> [2]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
=> [1,1,1]
=> [1,1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [2,1,1]
=> [1,1]
=> 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [7,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
=> [4,2]
=> [2]
=> 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
=> [5,2]
=> [2]
=> 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,1]
=> [1]
=> 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,1,1]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [5,1]
=> [1]
=> 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3]
=> [3]
=> 1 = 2 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [6,1]
=> [1]
=> 1 = 2 - 1
Description
The number of distinct irreducible representations contained in the higher Lie character for an integer partition.
The following 35 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
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. 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. St000225Difference between largest and smallest parts in a partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St001175The size of a partition minus the hook length of the base cell. 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. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000929The constant term of the character polynomial of an integer partition. St000944The 3-degree of an integer partition. 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 $eA$. 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. 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. 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. 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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