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Matching statistic: St000264
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00223: Permutations —runsort⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,2,3,5},{4},{6}}
=> [2,3,5,4,1,6] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,2,3},{4},{5,6}}
=> [2,3,1,4,6,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
{{1,2,3},{4},{5},{6}}
=> [2,3,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,2,4,5},{3},{6}}
=> [2,4,3,5,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2,4},{3,6},{5}}
=> [2,4,6,1,5,3] => [1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2,4},{3},{5,6}}
=> [2,4,3,1,6,5] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2,4},{3},{5},{6}}
=> [2,4,3,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3
{{1,2,5},{3,4},{6}}
=> [2,5,4,3,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2},{3,4,5,6}}
=> [2,1,4,5,6,3] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,2},{3,4,5},{6}}
=> [2,1,4,5,3,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,2,6},{3,4},{5}}
=> [2,6,4,3,5,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2},{3,4,6},{5}}
=> [2,1,4,6,5,3] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
{{1,2,5},{3},{4},{6}}
=> [2,5,3,4,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2},{3,5},{4,6}}
=> [2,1,5,6,3,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,2,6},{3},{4,5}}
=> [2,6,3,5,4,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,2},{3},{4,5,6}}
=> [2,1,3,5,6,4] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
{{1,3,4,5},{2},{6}}
=> [3,2,4,5,1,6] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,3,4},{2,5,6}}
=> [3,5,4,1,6,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,3,4},{2,5},{6}}
=> [3,5,4,1,2,6] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,3,4},{2},{5,6}}
=> [3,2,4,1,6,5] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,3,4},{2},{5},{6}}
=> [3,2,4,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3
{{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,3},{2,4,5},{6}}
=> [3,4,1,5,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
{{1,3},{2,4},{5},{6}}
=> [3,4,1,2,5,6] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,3,5},{2},{4},{6}}
=> [3,2,5,4,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,3},{2,5,6},{4}}
=> [3,5,1,4,6,2] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
{{1,3},{2,5},{4,6}}
=> [3,5,1,6,2,4] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,3},{2},{4,5,6}}
=> [3,2,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,3},{2,6},{4},{5}}
=> [3,6,1,4,5,2] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,3},{2},{4},{5,6}}
=> [3,2,1,4,6,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
{{1,3},{2},{4},{5},{6}}
=> [3,2,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,4,5,6},{2,3}}
=> [4,3,2,5,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,4,5},{2,3},{6}}
=> [4,3,2,5,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,4},{2,3,5,6}}
=> [4,3,5,1,6,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,4},{2,3,5},{6}}
=> [4,3,5,1,2,6] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,4},{2,3},{5},{6}}
=> [4,3,2,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,5},{2,3},{4},{6}}
=> [5,3,2,4,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1},{2,3,5},{4,6}}
=> [1,3,5,6,2,4] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
{{1,4,5},{2},{3},{6}}
=> [4,2,3,5,1,6] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
{{1,4,6},{2},{3,5}}
=> [4,2,5,6,3,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4
{{1,4},{2},{3,5,6}}
=> [4,2,5,1,6,3] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St000741
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Mp00223: Permutations —runsort⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 4 - 1
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,2,3,5},{4},{6}}
=> [2,3,5,4,1,6] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,2,3},{4},{5,6}}
=> [2,3,1,4,6,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,2,3},{4},{5},{6}}
=> [2,3,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,2,4,5},{3},{6}}
=> [2,4,3,5,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2,4},{3,6},{5}}
=> [2,4,6,1,5,3] => [1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2,4},{3},{5,6}}
=> [2,4,3,1,6,5] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2,4},{3},{5},{6}}
=> [2,4,3,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
{{1,2,5},{3,4},{6}}
=> [2,5,4,3,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2},{3,4,5,6}}
=> [2,1,4,5,6,3] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,2},{3,4,5},{6}}
=> [2,1,4,5,3,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,2,6},{3,4},{5}}
=> [2,6,4,3,5,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2},{3,4,6},{5}}
=> [2,1,4,6,5,3] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,2,5},{3},{4},{6}}
=> [2,5,3,4,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2},{3,5},{4,6}}
=> [2,1,5,6,3,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,2,6},{3},{4,5}}
=> [2,6,3,5,4,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2},{3},{4,5,6}}
=> [2,1,3,5,6,4] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,3,4,5},{2},{6}}
=> [3,2,4,5,1,6] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,3,4},{2,5,6}}
=> [3,5,4,1,6,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,3,4},{2,5},{6}}
=> [3,5,4,1,2,6] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,3,4},{2},{5,6}}
=> [3,2,4,1,6,5] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,3,4},{2},{5},{6}}
=> [3,2,4,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 3 - 1
{{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,3},{2,4,5},{6}}
=> [3,4,1,5,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,3},{2,4},{5},{6}}
=> [3,4,1,2,5,6] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,3,5},{2},{4},{6}}
=> [3,2,5,4,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,3},{2,5,6},{4}}
=> [3,5,1,4,6,2] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,3},{2,5},{4,6}}
=> [3,5,1,6,2,4] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,3},{2},{4,5,6}}
=> [3,2,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,3},{2,6},{4},{5}}
=> [3,6,1,4,5,2] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,3},{2},{4},{5,6}}
=> [3,2,1,4,6,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,3},{2},{4},{5},{6}}
=> [3,2,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,4,5,6},{2,3}}
=> [4,3,2,5,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,4,5},{2,3},{6}}
=> [4,3,2,5,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,4},{2,3,5,6}}
=> [4,3,5,1,6,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,4},{2,3,5},{6}}
=> [4,3,5,1,2,6] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,4},{2,3},{5},{6}}
=> [4,3,2,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,5},{2,3},{4},{6}}
=> [5,3,2,4,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1},{2,3,5},{4,6}}
=> [1,3,5,6,2,4] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,4,5},{2},{3},{6}}
=> [4,2,3,5,1,6] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,4,6},{2},{3,5}}
=> [4,2,5,6,3,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1,4},{2},{3,5,6}}
=> [4,2,5,1,6,3] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,4},{2},{3,5},{6}}
=> [4,2,5,1,3,6] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,4},{2},{3,6},{5}}
=> [4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1,4},{2},{3},{5},{6}}
=> [4,2,3,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1},{2,4,5},{3,6}}
=> [1,4,6,5,2,3] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1},{2,4,6},{3,5}}
=> [1,4,5,6,3,2] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1},{2,4},{3,5,6}}
=> [1,4,5,2,6,3] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1},{2,4},{3,5},{6}}
=> [1,4,5,2,3,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1},{2,4},{3,6},{5}}
=> [1,4,6,2,5,3] => [1,4,6,2,5,3] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,5},{2},{3,4},{6}}
=> [5,2,4,3,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1},{2,5},{3,4},{6}}
=> [1,5,4,3,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1},{2,6},{3,4},{5}}
=> [1,6,4,3,5,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1},{2,5},{3,6},{4}}
=> [1,5,6,4,2,3] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1},{2,5},{3},{4,6}}
=> [1,5,3,6,2,4] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1},{2,5},{3},{4},{6}}
=> [1,5,3,4,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 1
{{1},{2},{3,5},{4,6}}
=> [1,2,5,6,3,4] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 4 - 1
{{1},{2,6},{3},{4,5}}
=> [1,6,3,5,4,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
{{1,2,3,4,5},{6},{7}}
=> [2,3,4,5,1,6,7] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ? = 4 - 1
{{1,2,3,4,6},{5},{7}}
=> [2,3,4,6,5,1,7] => [1,7,2,3,4,6,5] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
{{1,2,3,4},{5,6,7}}
=> [2,3,4,1,6,7,5] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ? = 4 - 1
{{1,2,3,4},{5},{6,7}}
=> [2,3,4,1,5,7,6] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ? = 4 - 1
{{1,2,3,4},{5},{6},{7}}
=> [2,3,4,1,5,6,7] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ? = 4 - 1
{{1,2,3,5,6},{4},{7}}
=> [2,3,5,4,6,1,7] => [1,7,2,3,5,4,6] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
{{1,2,3,5},{4,6,7}}
=> [2,3,5,6,1,7,4] => [1,7,2,3,5,6,4] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
{{1,2,3,5},{4,6},{7}}
=> [2,3,5,6,1,4,7] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 4 - 1
{{1,2,3,5},{4,7},{6}}
=> [2,3,5,7,1,6,4] => [1,6,2,3,5,7,4] => ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
{{1,2,3,5},{4},{6,7}}
=> [2,3,5,4,1,7,6] => [1,7,2,3,5,4,6] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
{{1,2,3,5},{4},{6},{7}}
=> [2,3,5,4,1,6,7] => [1,6,7,2,3,5,4] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ? = 3 - 1
{{1,2,3,6},{4,5},{7}}
=> [2,3,6,5,4,1,7] => [1,7,2,3,6,4,5] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
{{1,2,3},{4,5,6,7}}
=> [2,3,1,5,6,7,4] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ? = 4 - 1
Description
The Colin de Verdière graph invariant.
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