Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000741
(load all 4 compositions to match this statistic)
Mapping
St000741: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 1
([(0,1)],2)
 => 1
([],3)
 => 1
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => 1
([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(2,3)],4)
 => 1
([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([],5)
 => 1
([(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(3,4)],5)
 => 1
([(0,1),(2,4),(3,4)],5)
 => 1
([(2,3),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([],6)
 => 1
([(3,5),(4,5)],6)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(2,5),(3,4),(4,5)],6)
 => 1
([(1,2),(3,5),(4,5)],6)
 => 1
([(3,4),(3,5),(4,5)],6)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2
Description
The Colin de Verdière graph invariant.
Matching statistic: St000264
Mapping
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 26%●distinct values known / distinct values provided: 17%
Values
([],1)
 => [1] => [1] => ([],1)
 => ? = 0 + 1
([],2)
 => [2] => [1] => ([],1)
 => ? = 1 + 1
([(0,1)],2)
 => [1,1] => [2] => ([],2)
 => ? = 1 + 1
([],3)
 => [3] => [1] => ([],1)
 => ? = 1 + 1
([(0,2),(1,2)],3)
 => [2,1] => [1,1] => ([(0,1)],2)
 => ? = 2 + 1
([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => [3] => ([],3)
 => ? = 2 + 1
([],4)
 => [4] => [1] => ([],1)
 => ? = 1 + 1
([(1,3),(2,3)],4)
 => [3,1] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(0,3),(1,3),(2,3)],4)
 => [3,1] => [1,1] => ([(0,1)],2)
 => ? = 2 + 1
([(0,3),(1,2),(2,3)],4)
 => [2,2] => [2] => ([],2)
 => ? = 1 + 1
([(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => [4] => ([],4)
 => ? = 3 + 1
([],5)
 => [5] => [1] => ([],1)
 => ? = 1 + 1
([(2,4),(3,4)],5)
 => [4,1] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,1] => [1,1] => ([(0,1)],2)
 => ? = 2 + 1
([(1,4),(2,3),(3,4)],5)
 => [3,2] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(0,1),(2,4),(3,4)],5)
 => [3,2] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? = 3 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [3,2] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => ([(2,3)],4)
 => ? = 3 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => ([(2,3)],4)
 => ? = 3 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => ([(2,3)],4)
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => ([(2,3)],4)
 => ? = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => [5] => ([],5)
 => ? = 4 + 1
([],6)
 => [6] => [1] => ([],1)
 => ? = 1 + 1
([(3,5),(4,5)],6)
 => [5,1] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1] => [1,1] => ([(0,1)],2)
 => ? = 2 + 1
([(2,5),(3,4),(4,5)],6)
 => [4,2] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(1,2),(3,5),(4,5)],6)
 => [4,2] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [4,2] => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St001629
Mapping
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 17% ●values known / values provided: 26%●distinct values known / distinct values provided: 17%
Values
([],1)
 => [1] => [1] => [1] => ? = 0 - 1
([],2)
 => [2] => [1] => [1] => ? = 1 - 1
([(0,1)],2)
 => [1,1] => [2] => [1] => ? = 1 - 1
([],3)
 => [3] => [1] => [1] => ? = 1 - 1
([(0,2),(1,2)],3)
 => [2,1] => [1,1] => [2] => ? = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => [3] => [1] => ? = 2 - 1
([],4)
 => [4] => [1] => [1] => ? = 1 - 1
([(1,3),(2,3)],4)
 => [3,1] => [1,1] => [2] => ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => [3,1] => [1,1] => [2] => ? = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [2,2] => [2] => [1] => ? = 1 - 1
([(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => [4] => [1] => ? = 3 - 1
([],5)
 => [5] => [1] => [1] => ? = 1 - 1
([(2,4),(3,4)],5)
 => [4,1] => [1,1] => [2] => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,1] => [1,1] => [2] => ? = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [3,2] => [1,1] => [2] => ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => [3,2] => [1,1] => [2] => ? = 1 - 1
([(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,2] => [1,1] => ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [3,2] => [1,1] => [2] => ? = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => [1,1] => ? = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => [1,1] => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => [1,1] => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => [1,1] => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => [1,1] => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,1] => [1,1] => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => [1,1] => ? = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => [1,1] => ? = 3 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => [1,1] => ? = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,3] => [1,1] => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => [5] => [1] => ? = 4 - 1
([],6)
 => [6] => [1] => [1] => ? = 1 - 1
([(3,5),(4,5)],6)
 => [5,1] => [1,1] => [2] => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1] => [1,1] => [2] => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [4,2] => [1,1] => [2] => ? = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => [4,2] => [1,1] => [2] => ? = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [4,2] => [1,1] => [2] => ? = 1 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,2] => [1,1] => ? = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,1,2] => [1,1,1] => [3] => 1 = 2 - 1
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,1,1] => [3] => 1 = 2 - 1
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.