- FindStat

Your data matches 119 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000897
(load all 2 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
St000897: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => []
 => 0
([],2)
 => ([(0,1)],2)
 => [1]
 => 1
([(0,1)],2)
 => ([],2)
 => []
 => 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => [3]
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [2]
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => [1]
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => []
 => 0
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => [1]
 => 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3]
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => [2]
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => [1]
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [3]
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => [1]
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => [1]
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3]
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [3]
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => [1,1]
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => []
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [2]
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [10]
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [9]
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => [3]
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => [1]
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [3]
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => [1,1]
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => [3]
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => [1,1]
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => [3]
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => 1

Description

The number of different multiplicities of parts of an integer partition.

Matching statistic: St001335
(load all 6 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001335: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 69%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0
([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1)],2)
 => ([],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(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
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(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
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([],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)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(3,4)],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)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(2,3),(2,4)],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)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(0,3),(0,4)],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)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,2),(0,3),(0,4),(4,1)],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)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(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
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],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
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(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
([(2,4),(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)
 => ([(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
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(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
([(0,4),(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)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => ([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
 => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => ([(3,6),(4,5)],7)
 => ([(3,6),(4,5)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7)
 => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
 => ([(1,6),(2,5),(3,4)],7)
 => ([(1,6),(2,5),(3,4)],7)
 => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 1
([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7)
 => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)
 => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7)
 => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7)
 => ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
 => ([(2,3),(4,6),(5,6)],7)
 => ([(2,3),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7)
 => ([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
 => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1

Description

The cardinality of a minimal cycle-isolating set of a graph. Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$. This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains all cycles.

Matching statistic: St000260
(load all 5 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 57% ●values known / values provided: 57%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => [1] => ([],1)
 => 0
([],2)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => 1
([(0,1)],2)
 => ([],2)
 => [2] => ([],2)
 => ? = 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => [2,1] => ([(0,2),(1,2)],3)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1
([(0,2),(2,1)],3)
 => ([],3)
 => [3] => ([],3)
 => ? = 0
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => [1,3] => ([(2,3)],4)
 => ? = 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => [1,3] => ([(2,3)],4)
 => ? = 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => [1,3] => ([(2,3)],4)
 => ? = 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => [4] => ([],4)
 => ? = 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => [1,4] => ([(3,4)],5)
 => ? = 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(3,4)],5)
 => [1,4] => ([(3,4)],5)
 => ? = 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(1,4),(2,3)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(2,4),(3,4)],5)
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(3,4)],5)
 => [1,4] => ([(3,4)],5)
 => ? = 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(2,4),(3,4)],5)
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(2,4),(3,4)],5)
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => [5] => ([],5)
 => ? = 0
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => [1,4] => ([(3,4)],5)
 => ? = 1
([(2,3),(2,4),(2,5)],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)
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(2,3),(2,4),(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)
 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1

Description

The radius of a connected graph. This is the minimum eccentricity of any vertex.

Matching statistic: St000379
(load all 2 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000379: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%

Values

([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 1
([],2)
 => ([(0,1)],2)
 => ([],2)
 => ([],2)
 => 0 = 1 - 1
([(0,1)],2)
 => ([],2)
 => ([(0,1)],2)
 => ([],1)
 => ? = 0 - 1
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([],2)
 => 0 = 1 - 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ? = 0 - 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],4)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([],3)
 => 0 = 1 - 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 0 = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 1 - 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => 0 = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 0 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],5)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([],4)
 => 0 = 1 - 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 0 = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(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)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => 0 = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 1 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0 = 1 - 1
([(0,3),(1,2),(1,3),(2,4),(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)
 => ([],1)
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 0 = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(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)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,4),(2,3),(3,1),(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)
 => ? = 0 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(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)
 => ([],1)
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],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 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(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)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => ([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],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)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],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)
 => ([],1)
 => ? = 1 - 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],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 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],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)
 => ([],1)
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],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 - 1

Description

The number of Hamiltonian cycles in a graph. A Hamiltonian cycle in a graph $G$ is a subgraph (this is, a subset of the edges) that is a cycle which contains every vertex of $G$. Since it is unclear whether the graph on one vertex is Hamiltonian, the statistic is undefined for this graph.

Matching statistic: St000456
(load all 4 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 39%●distinct values known / distinct values provided: 33%

Values

([],1)
 => ([],1)
 => ([],1)
 => ? = 0
([],2)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1
([(0,1)],2)
 => ([],2)
 => ([],2)
 => ? = 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ? = 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],3)
 => ? = 0
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ? = 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([],3)
 => ? = 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([],3)
 => ? = 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([],3)
 => ? = 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ? = 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ? = 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => ? = 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],4)
 => ? = 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? = 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ? = 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([],4)
 => ? = 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ? = 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => ? = 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ? = 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => ? = 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(3,4)],5)
 => ([],4)
 => ? = 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,4),(4,5),(5,2),(5,3)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,5),(2,5),(5,3),(5,4)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,5),(2,5),(3,5),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
 => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 1
([(1,5),(2,5),(3,4),(5,3)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 1

Description

The monochromatic index of a connected graph. This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path. For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.

Matching statistic: St001890
(load all 3 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00243: Graphs —weak duplicate order⟶ Posets
St001890: Posets ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 33%

Values

([],1)
 => ([],1)
 => ([],1)
 => ? = 0
([],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],1)
 => ? = 0
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],3)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],2)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],2)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],1)
 => ? = 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],4)
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(2,3)],4)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ([],1)
 => ? = 0
([(2,3),(2,4),(2,5)],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)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(1,5),(2,5),(5,3),(5,4)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 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),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(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)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4)],6)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(1,5),(2,4),(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)
 => ([(4,5)],6)
 => ? = 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4)],6)
 => ? = 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4)],6)
 => ? = 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(5,4)],6)
 => ? = 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1

Description

The maximum magnitude of the Möbius function of a poset. The '''Möbius function''' of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value $\mu(x, y)$ is equal to the signed sum of chains from $x$ to $y$, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.

Matching statistic: St000455
(load all 6 compositions to match this statistic)

Mapping

Mp00205: Posets —maximal antichains⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 29% ●values known / values provided: 29%●distinct values known / distinct values provided: 33%

Values

([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 0 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 0 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(4,2),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(1,5),(2,3),(2,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,5),(1,2),(1,3),(1,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => 0 = 1 - 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(3,5),(4,2)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1

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: St001737

Mapping

Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St001737: Permutations ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 67%

Values

([],1)
 => [1]
 => [[1]]
 => [1] => 0
([],2)
 => [1,1]
 => [[1],[2]]
 => [2,1] => 1
([(0,1)],2)
 => [2]
 => [[1,2]]
 => [1,2] => 0
([],3)
 => [1,1,1]
 => [[1],[2],[3]]
 => [3,2,1] => 1
([(1,2)],3)
 => [2,1]
 => [[1,2],[3]]
 => [3,1,2] => 1
([(0,1),(0,2)],3)
 => [2,1]
 => [[1,2],[3]]
 => [3,1,2] => 1
([(0,2),(2,1)],3)
 => [3]
 => [[1,2,3]]
 => [1,2,3] => 0
([(0,2),(1,2)],3)
 => [2,1]
 => [[1,2],[3]]
 => [3,1,2] => 1
([],4)
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => [4,3,2,1] => 1
([(2,3)],4)
 => [2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => 1
([(1,2),(1,3)],4)
 => [2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => 1
([(0,1),(0,2),(0,3)],4)
 => [2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => 1
([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => 1
([(1,2),(2,3)],4)
 => [3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => 1
([(0,3),(3,1),(3,2)],4)
 => [3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => 1
([(1,3),(2,3)],4)
 => [2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => 1
([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => 1
([(0,3),(1,3),(2,3)],4)
 => [2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => 1
([(0,3),(1,2)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => [3,4,1,2] => 1
([(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => [3,4,1,2] => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => [3,4,1,2] => 1
([(0,3),(2,1),(3,2)],4)
 => [4]
 => [[1,2,3,4]]
 => [1,2,3,4] => 0
([(0,3),(1,2),(2,3)],4)
 => [3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => 1
([],5)
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => 1
([(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 1
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 1
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(1,3),(1,4),(4,2)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [4,1]
 => [[1,2,3,4],[5]]
 => [5,1,2,3,4] => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [3,2]
 => [[1,2,3],[4,5]]
 => [4,5,1,2,3] => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [[1,2,3],[4,5]]
 => [4,5,1,2,3] => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,2]
 => [[1,2,3],[4,5]]
 => [4,5,1,2,3] => 1
([(2,3),(3,4)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(1,4),(4,2),(4,3)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 1
([(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => [3,2]
 => [[1,2,3],[4,5]]
 => [4,5,1,2,3] => 1
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 1
([(0,4),(1,4),(2,3)],5)
 => [2,2,1]
 => [[1,2],[3,4],[5]]
 => [5,3,4,1,2] => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,1]
 => [[1,2],[3,4],[5]]
 => [5,3,4,1,2] => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => ? = 1
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => [5,1,1]
 => [[1,2,3,4,5],[6],[7]]
 => [7,6,1,2,3,4,5] => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ? = 1
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
 => [4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ? = 1

Description

The number of descents of type 2 in a permutation. A position $i\in[1,n-1]$ is a descent of type 2 of a permutation $\pi$ of $n$ letters, if it is a descent and if $\pi(j) < \pi(i)$ for all $j < i$.

Matching statistic: St000259
(load all 5 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([(0,1)],2)
 => ([],2)
 => ([],1)
 => 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(3,4)],5)
 => ([(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)
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(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)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
 => ([(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
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(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
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
 => ([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
 => ([(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
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
 => ([(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
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
 => ([(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
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
 => ([(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
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => ([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)
 => ([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
 => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1

Description

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

Matching statistic: St000535
(load all 5 compositions to match this statistic)

Mapping

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000535: Graphs ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([(0,1)],2)
 => ([],2)
 => ([],1)
 => 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(3,4)],5)
 => ([(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)
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(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)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
 => ([(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
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(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
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
 => ([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
 => ([(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
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
 => ([(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
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
 => ([(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
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
 => ([(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
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7)
 => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
 => ([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)
 => ([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
 => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 1

Description

The rank-width of a graph.

The following 109 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001271The competition number of a graph. St001333The cardinality of a minimal edge-isolating set of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001393The induced matching number of a graph. St001512The minimum rank of a graph. St000258The burning number of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000918The 2-limited packing number of a graph. St001093The detour number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001674The number of vertices of the largest induced star graph in the graph. St000256The number of parts from which one can substract 2 and still get an integer partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000480The number of lower covers of a partition in dominance order. St000741The Colin de Verdière graph invariant. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001280The number of parts of an integer partition that are at least two. St001777The number of weak descents in an integer composition. St001931The weak major index of an integer composition regarded as a word. St000378The diagonal inversion number of an integer partition. St000485The length of the longest cycle of a permutation. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001486The number of corners of the ribbon associated with an integer composition. St001642The Prague dimension of a graph. St001746The coalition number of a graph. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000264The girth of a graph, which is not a tree. St000284The Plancherel distribution on integer partitions. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000993The multiplicity of the largest part of an integer partition. St001128The exponens consonantiae of a partition. St001568The smallest positive integer that does not appear twice in the partition. St000567The sum of the products of all pairs of parts. St000699The toughness times the least common multiple of 1,. St000929The constant term of the character polynomial of an integer partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for vertex labelled trees. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a 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 $eA$. St001281The normalized isoperimetric number of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001592The maximal number of simple paths between any two different vertices of a graph. St001060The distinguishing index of a graph. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000781The number of proper colouring schemes of a Ferrers diagram. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. 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. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001624The breadth of a lattice. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St000298The order dimension or Dushnik-Miller dimension of a poset. St001720The minimal length of a chain of small intervals in a lattice. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001498The normalised height of a Nakayama algebra with magnitude 1. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ 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. St001118The acyclic chromatic index of a graph. St001545The second Elser number of a connected graph. St000464The Schultz index of a connected graph. St000272The treewidth of a graph. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001331The size of the minimal feedback vertex set. St001358The largest degree of a regular subgraph of a graph. St001638The book thickness of a graph. St001644The dimension of a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001826The maximal number of leaves on a vertex of a graph. St001962The proper pathwidth of a graph. St000544The cop number of a graph. St001029The size of the core of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001883The mutual visibility number of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph.