searching the database
Your data matches 12 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000260
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,1)],2)
=> ([],1)
=> ([],1)
=> 0
([],3)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,2)],3)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> 0
([],4)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(2,3)],4)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,3),(2,3)],4)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2)],4)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,3),(1,2),(2,3)],4)
=> ([],1)
=> ([],1)
=> 0
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(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)
=> 1
([(3,4)],5)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(2,4),(3,4)],5)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3)],5)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,4),(2,3),(3,4)],5)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,1),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,1)],2)
=> 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)
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(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)
=> 1
([(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)
=> 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 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)
=> 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)
=> 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)
=> 1
([(4,5)],6)
=> ([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(3,5),(4,5)],6)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> 0
([(2,5),(3,4)],6)
=> ([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 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)
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(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)
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> 0
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St001738
Values
([],1)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([],2)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,1)],2)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([],3)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,2)],3)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,2),(1,2)],3)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([],4)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(2,3)],4)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,3),(2,3)],4)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(0,3),(1,2)],4)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,3),(1,2),(2,3)],4)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
([],5)
=> ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(3,4)],5)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(2,4),(3,4)],5)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(1,4),(2,3)],5)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,4),(2,3),(3,4)],5)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,1),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 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),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 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)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([],6)
=> ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 2
([(4,5)],6)
=> ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(3,5),(4,5)],6)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(2,5),(3,4)],6)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 2
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(0,5),(1,4),(2,3)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(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)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 2
([(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)
=> ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 2
([(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)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 2 = 0 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(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)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(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)
=> ? = 1 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 2
([(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)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(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)
=> ? = 1 + 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(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)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 + 2
([(3,6),(4,6),(5,6)],7)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 1 + 2
([(2,6),(3,6),(4,6),(5,6)],7)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 3 = 1 + 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> 3 = 1 + 2
Description
The minimal order of a graph which is not an induced subgraph of the given graph.
For example, the graph with two isolated vertices is not an induced subgraph of the complete graph on three vertices.
By contrast, the minimal number of vertices of a graph which is not a subgraph of a graph is one plus the clique number [[St000097]].
Matching statistic: St000781
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 0
([],2)
=> [1,1]
=> [1]
=> []
=> ? = 1
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? = 0
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? = 1
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? = 0
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? = 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1
([],5)
=> [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
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [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]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(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)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(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]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [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]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(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]
=> 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]
=> []
=> ?
=> ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [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]
=> []
=> ?
=> ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [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]
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(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
([(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
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 1
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 1
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 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
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 0
([],2)
=> [1,1]
=> [1]
=> []
=> ? = 1
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? = 0
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? = 1
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? = 0
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? = 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1
([],5)
=> [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
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [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]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(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)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(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]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [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]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(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]
=> 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]
=> []
=> ?
=> ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [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]
=> []
=> ?
=> ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [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]
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(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
([(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
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 1
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 1
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Matching statistic: St001934
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001934: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001934: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 0
([],2)
=> [1,1]
=> [1]
=> []
=> ? = 1
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? = 0
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? = 1
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? = 0
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? = 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1
([],5)
=> [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
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [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]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(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)],5)
=> [5]
=> []
=> ?
=> ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 2
([(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]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [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]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(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]
=> 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]
=> []
=> ?
=> ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [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]
=> []
=> ?
=> ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [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]
=> 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(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
([(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
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 1
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 1
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 1
Description
The number of monotone factorisations of genus zero of a permutation of given cycle type.
A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions
$$
(a_1, b_1),\dots,(a_r, b_r)
$$
with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$.
For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.
Matching statistic: St000205
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000205: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000205: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 0 - 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? = 0 - 1
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? = 0 - 1
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0 - 1
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0 - 1
([(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]
=> 0 = 1 - 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1 - 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(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)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1 - 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)
=> [5]
=> []
=> ?
=> ? = 2 - 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]
=> 0 = 1 - 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 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]
=> []
=> ? = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(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]
=> 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [3,3]
=> [3]
=> []
=> ? = 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]
=> []
=> ?
=> ? = 0 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 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]
=> []
=> ?
=> ? = 0 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 0 = 1 - 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]
=> []
=> ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 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]
=> []
=> ? = 1 - 1
([(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
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(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)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 0 = 1 - 1
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 1 - 1
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 0 = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight.
Given $\lambda$ count how many ''integer partitions'' $w$ (weight) there are, such that
$P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.
Matching statistic: St000206
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000206: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000206: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 0 - 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? = 0 - 1
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? = 0 - 1
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0 - 1
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0 - 1
([(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]
=> 0 = 1 - 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1 - 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(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)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1 - 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)
=> [5]
=> []
=> ?
=> ? = 2 - 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]
=> 0 = 1 - 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 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]
=> []
=> ? = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(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]
=> 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [3,3]
=> [3]
=> []
=> ? = 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]
=> []
=> ?
=> ? = 0 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 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]
=> []
=> ?
=> ? = 0 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 0 = 1 - 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]
=> []
=> ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 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]
=> []
=> ? = 1 - 1
([(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
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(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)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 0 = 1 - 1
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 1 - 1
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 0 = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight.
Given $\lambda$ count how many ''integer compositions'' $w$ (weight) there are, such that
$P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.
See also [[St000205]].
Each value in this statistic is greater than or equal to corresponding value in [[St000205]].
Matching statistic: St001175
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001175: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001175: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 0 - 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? = 0 - 1
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? = 0 - 1
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0 - 1
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? = 0 - 1
([(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]
=> 0 = 1 - 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1 - 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(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)],5)
=> [5]
=> []
=> ?
=> ? = 0 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? = 1 - 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)
=> [5]
=> []
=> ?
=> ? = 2 - 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]
=> 0 = 1 - 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 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]
=> []
=> ? = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(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]
=> 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [3,3]
=> [3]
=> []
=> ? = 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]
=> []
=> ?
=> ? = 0 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 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]
=> []
=> ?
=> ? = 0 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 0 = 1 - 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]
=> []
=> ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 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]
=> []
=> ? = 1 - 1
([(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
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(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)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [6]
=> []
=> ?
=> ? = 0 - 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 0 = 1 - 1
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 0 = 1 - 1
([(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,6),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,6),(4,5)],7)
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(3,6),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,3),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(4,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,5),(3,6),(4,5),(4,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> [3,3,1]
=> [3,1]
=> [1]
=> 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,1,1,1]
=> [1,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,6),(2,5),(3,4)],7)
=> [2,2,2,1]
=> [2,2,1]
=> [2,1]
=> 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
=> [3,2,2]
=> [2,2]
=> [2]
=> 0 = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1]
=> [2,1,1]
=> [1,1]
=> 0 = 1 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [5,1,1]
=> [1,1]
=> [1]
=> 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1]
=> [2,1]
=> [1]
=> 0 = 1 - 1
Description
The size of a partition minus the hook length of the base cell.
This is, the number of boxes in the diagram of a partition that are neither in the first row nor in the first column.
Matching statistic: St000454
Values
([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([],2)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,1)],2)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([],3)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(1,2)],3)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,2),(1,2)],3)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([],4)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(2,3)],4)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(1,3),(2,3)],4)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,3),(1,2)],4)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,3),(1,2),(2,3)],4)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
([],5)
=> ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
([(3,4)],5)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(2,4),(3,4)],5)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,3)],5)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(1,4),(2,3),(3,4)],5)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,1),(2,4),(3,4)],5)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 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),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ? = 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)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 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)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
([],6)
=> ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 1
([(4,5)],6)
=> ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
([(3,5),(4,5)],6)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,5),(3,4)],6)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([(0,2),(1,2)],3)
=> ? = 1 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 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)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 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)
=> ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 1 + 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(3,6),(4,6),(5,6)],7)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(3,6),(4,5),(5,6)],7)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(2,3),(4,6),(5,6)],7)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(1,6),(2,5),(3,4)],7)
=> ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Matching statistic: St001630
Values
([],1)
=> ([],1)
=> ([],1)
=> ? = 0 + 1
([],2)
=> ([],1)
=> ([],1)
=> ? = 1 + 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 0 + 1
([],3)
=> ([],1)
=> ([],1)
=> ? = 1 + 1
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 0 + 1
([],4)
=> ([],1)
=> ([],1)
=> ? = 1 + 1
([(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 0 + 1
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 1
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([],5)
=> ([],1)
=> ([],1)
=> ? = 1 + 1
([(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 0 + 1
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
=> ? = 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)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,25),(2,13),(2,14),(2,15),(2,25),(3,10),(3,11),(3,12),(3,25),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,21),(7,24),(7,29),(8,19),(8,22),(8,29),(9,20),(9,23),(9,29),(10,26),(10,29),(11,27),(11,29),(12,28),(12,29),(13,19),(13,21),(13,26),(14,20),(14,21),(14,27),(15,19),(15,20),(15,28),(16,22),(16,24),(16,26),(17,23),(17,24),(17,27),(18,22),(18,23),(18,28),(19,30),(20,30),(21,30),(22,30),(23,30),(24,30),(25,26),(25,27),(25,28),(26,30),(27,30),(28,30),(29,30)],31)
=> ? = 2 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? = 1 + 1
([],6)
=> ([],1)
=> ([],1)
=> ? = 1 + 1
([(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 0 + 1
([(2,5),(3,4)],6)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
([(1,2),(3,5),(4,5)],6)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? = 1 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? = 0 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 1 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 1 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(3,6),(4,5)],7)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,3),(4,6),(5,6)],7)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(4,5),(4,6),(5,6)],7)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,6),(2,6),(3,5),(4,5)],7)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
The following 2 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!