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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St001667
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St001667: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 2
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 1
[2,1,3,4] => 2
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 1
[3,2,4,1] => 2
[3,4,1,2] => 2
[3,4,2,1] => 2
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 2
[4,3,2,1] => 2
[1,2,3,4,5] => 2
[1,2,3,5,4] => 2
[1,2,4,3,5] => 2
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 2
[1,3,2,4,5] => 2
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 2
[1,4,2,3,5] => 2
[1,4,2,5,3] => 2
[1,4,3,2,5] => 2
[1,4,3,5,2] => 2
[1,4,5,2,3] => 2
Description
The maximal size of a pair of weak twins for a permutation.
A pair of weak twins in a permutation is a pair of two disjoint subsequences of the same length with the same descent pattern. More formally, a pair of weak twins of size $k$ for a permutation $\pi$ of length $n$ are two disjoint lists $1 \leq i_1 < \dots < i_k \leq n$ and $1 \leq j_1 < \dots < j_k \leq n$ such that $\pi(i_a) < \pi(i_{a+1})$ if and only if $\pi(j_a) < \pi(j_{a+1})$ for all $1 \leq a < k$.
Matching statistic: St001603
Mp00223: Permutations —runsort⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 25%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 25%
Values
[1] => [1] => [1]
=> []
=> ? = 0 - 2
[1,2] => [1,2] => [2]
=> []
=> ? = 1 - 2
[2,1] => [1,2] => [2]
=> []
=> ? = 1 - 2
[1,2,3] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? = 1 - 2
[2,1,3] => [1,3,2] => [2,1]
=> [1]
=> ? = 1 - 2
[2,3,1] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[3,1,2] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[3,2,1] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[1,2,3,4] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[1,2,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[1,3,2,4] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[1,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> ? = 2 - 2
[1,4,2,3] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[1,4,3,2] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 1 - 2
[2,1,3,4] => [1,3,4,2] => [3,1]
=> [1]
=> ? = 2 - 2
[2,1,4,3] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[2,3,1,4] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[2,3,4,1] => [1,2,3,4] => [4]
=> []
=> ? = 1 - 2
[2,4,1,3] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[2,4,3,1] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,1,2,4] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,1,4,2] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,2,1,4] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 1 - 2
[3,2,4,1] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,4,1,2] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[3,4,2,1] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[4,1,2,3] => [1,2,3,4] => [4]
=> []
=> ? = 1 - 2
[4,1,3,2] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[4,2,1,3] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[4,2,3,1] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[4,3,1,2] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[4,3,2,1] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[1,2,3,4,5] => [1,2,3,4,5] => [5]
=> []
=> ? = 2 - 2
[1,2,3,5,4] => [1,2,3,5,4] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,4,3,5] => [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,4,5,3] => [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,5,3,4] => [1,2,5,3,4] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,5,4,3] => [1,2,5,3,4] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,2,4,5] => [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 2 - 2
[1,3,4,2,5] => [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,4,5,2] => [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 2 - 2
[1,3,5,4,2] => [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 2 - 2
[1,4,2,3,5] => [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 2 - 2
[1,4,3,2,5] => [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 2 - 2
[1,4,3,5,2] => [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,4,5,2,3] => [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 2 - 2
[1,3,6,2,5,4] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,6,4,2,5] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,4,6,2,5,3] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,4,6,3,2,5] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,5,6,2,4,3] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,5,6,3,2,4] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,4,1,5,6,3] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,4,3,1,5,6] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,1,3,6,4] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,1,4,6,3] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,3,1,4,6] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,4,1,3,6] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,1,4,6,2,5] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,1,5,6,2,4] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,2,4,1,5,6] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,2,5,1,4,6] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[4,1,3,6,2,5] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[4,2,5,1,3,6] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,4,7,3,6,5] => [1,2,4,7,3,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,4,7,5,3,6] => [1,2,4,7,3,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,5,7,3,6,4] => [1,2,5,7,3,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,5,7,4,3,6] => [1,2,5,7,3,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,6,7,3,5,4] => [1,2,6,7,3,5,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,6,7,4,3,5] => [1,2,6,7,3,5,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,5,7,4,6] => [1,3,2,5,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,5,7,6,4] => [1,3,2,5,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,4,7,5] => [1,3,2,6,4,7,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,5,4,7] => [1,3,2,6,4,7,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,7,4,5] => [1,3,2,6,7,4,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,7,5,4] => [1,3,2,6,7,4,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,7,4,6,5] => [1,3,2,7,4,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,2,7,5,4,6] => [1,3,2,7,4,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,4,7,2,6,5] => [1,3,4,7,2,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,4,7,5,2,6] => [1,3,4,7,2,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,5,2,4,7,6] => [1,3,5,2,4,7,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,2,7,4,6] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,2,7,6,4] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,4,2,7,6] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,4,6,2,7] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,4,7,6,2] => [1,3,5,2,4,7,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,2,4,6] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,2,6,4] => [1,3,5,7,2,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,5,7,4,2,6] => [1,3,5,7,2,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,5,7,4,6,2] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,6,2,4] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,6,4,2] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,6,2,4,7,5] => [1,3,6,2,4,7,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,6,2,5,4,7] => [1,3,6,2,5,4,7] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,6,2,5,7,4] => [1,3,6,2,5,7,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001605
Mp00223: Permutations —runsort⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 25%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 25%
Values
[1] => [1] => [1]
=> []
=> ? = 0 - 2
[1,2] => [1,2] => [2]
=> []
=> ? = 1 - 2
[2,1] => [1,2] => [2]
=> []
=> ? = 1 - 2
[1,2,3] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? = 1 - 2
[2,1,3] => [1,3,2] => [2,1]
=> [1]
=> ? = 1 - 2
[2,3,1] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[3,1,2] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[3,2,1] => [1,2,3] => [3]
=> []
=> ? = 1 - 2
[1,2,3,4] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[1,2,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[1,3,2,4] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[1,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> ? = 2 - 2
[1,4,2,3] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[1,4,3,2] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 1 - 2
[2,1,3,4] => [1,3,4,2] => [3,1]
=> [1]
=> ? = 2 - 2
[2,1,4,3] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[2,3,1,4] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[2,3,4,1] => [1,2,3,4] => [4]
=> []
=> ? = 1 - 2
[2,4,1,3] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[2,4,3,1] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,1,2,4] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,1,4,2] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,2,1,4] => [1,4,2,3] => [3,1]
=> [1]
=> ? = 1 - 2
[3,2,4,1] => [1,2,4,3] => [3,1]
=> [1]
=> ? = 2 - 2
[3,4,1,2] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[3,4,2,1] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[4,1,2,3] => [1,2,3,4] => [4]
=> []
=> ? = 1 - 2
[4,1,3,2] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[4,2,1,3] => [1,3,2,4] => [3,1]
=> [1]
=> ? = 2 - 2
[4,2,3,1] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[4,3,1,2] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[4,3,2,1] => [1,2,3,4] => [4]
=> []
=> ? = 2 - 2
[1,2,3,4,5] => [1,2,3,4,5] => [5]
=> []
=> ? = 2 - 2
[1,2,3,5,4] => [1,2,3,5,4] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,4,3,5] => [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,4,5,3] => [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,5,3,4] => [1,2,5,3,4] => [4,1]
=> [1]
=> ? = 2 - 2
[1,2,5,4,3] => [1,2,5,3,4] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,2,4,5] => [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 2 - 2
[1,3,4,2,5] => [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,4,5,2] => [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 2 - 2
[1,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 2 - 2
[1,3,5,4,2] => [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 2 - 2
[1,4,2,3,5] => [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 2 - 2
[1,4,3,2,5] => [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 2 - 2
[1,4,3,5,2] => [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 2 - 2
[1,4,5,2,3] => [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 2 - 2
[1,3,6,2,5,4] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,6,4,2,5] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,4,6,2,5,3] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,4,6,3,2,5] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,5,6,2,4,3] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,5,6,3,2,4] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,4,1,5,6,3] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,4,3,1,5,6] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,1,3,6,4] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,1,4,6,3] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,3,1,4,6] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[2,5,4,1,3,6] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,1,4,6,2,5] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,1,5,6,2,4] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,2,4,1,5,6] => [1,5,6,2,4,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[3,2,5,1,4,6] => [1,4,6,2,5,3] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[4,1,3,6,2,5] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[4,2,5,1,3,6] => [1,3,6,2,5,4] => [3,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,4,7,3,6,5] => [1,2,4,7,3,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,4,7,5,3,6] => [1,2,4,7,3,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,5,7,3,6,4] => [1,2,5,7,3,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,5,7,4,3,6] => [1,2,5,7,3,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,6,7,3,5,4] => [1,2,6,7,3,5,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,2,6,7,4,3,5] => [1,2,6,7,3,5,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,5,7,4,6] => [1,3,2,5,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,5,7,6,4] => [1,3,2,5,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,4,7,5] => [1,3,2,6,4,7,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,5,4,7] => [1,3,2,6,4,7,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,7,4,5] => [1,3,2,6,7,4,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,6,7,5,4] => [1,3,2,6,7,4,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,2,7,4,6,5] => [1,3,2,7,4,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,2,7,5,4,6] => [1,3,2,7,4,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,4,7,2,6,5] => [1,3,4,7,2,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,4,7,5,2,6] => [1,3,4,7,2,6,5] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,5,2,4,7,6] => [1,3,5,2,4,7,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,2,7,4,6] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,2,7,6,4] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,4,2,7,6] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,4,6,2,7] => [1,3,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,4,7,6,2] => [1,3,5,2,4,7,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,2,4,6] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,2,6,4] => [1,3,5,7,2,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,5,7,4,2,6] => [1,3,5,7,2,6,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,5,7,4,6,2] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,6,2,4] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,5,7,6,4,2] => [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,6,2,4,7,5] => [1,3,6,2,4,7,5] => [4,3]
=> [3]
=> 1 = 3 - 2
[1,3,6,2,5,4,7] => [1,3,6,2,5,4,7] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
[1,3,6,2,5,7,4] => [1,3,6,2,5,7,4] => [4,2,1]
=> [2,1]
=> 1 = 3 - 2
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the cyclic group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001393
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001393: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Mp00209: Permutations —pattern poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001393: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Values
[1] => [1] => ([],1)
=> ([],1)
=> 0
[1,2] => [2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 1
[2,1] => [1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 1
[1,2,3] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
[1,3,2] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
[2,1,3] => [3,2,1] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
[3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
[1,2,3,4] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[1,2,4,3] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[1,3,2,4] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[1,3,4,2] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[1,4,2,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? = 2
[1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 1
[2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[2,1,4,3] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[2,3,1,4] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1
[2,4,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[3,1,2,4] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[3,1,4,2] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1
[3,2,4,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[3,4,1,2] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[3,4,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[4,1,2,3] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 1
[4,1,3,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? = 2
[4,2,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[4,2,3,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[4,3,1,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[4,3,2,1] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[1,2,3,4,5] => [2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 2
[1,2,3,5,4] => [2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[1,2,4,3,5] => [2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2
[1,2,4,5,3] => [2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[1,2,5,3,4] => [2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? = 2
[1,2,5,4,3] => [2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? = 2
[1,3,2,4,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2
[1,3,2,5,4] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2
[1,3,4,2,5] => [2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2
[1,3,4,5,2] => [2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 2
[1,3,5,2,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(0,13),(0,14),(1,5),(1,6),(1,14),(2,3),(2,4),(2,13),(3,10),(3,11),(3,12),(4,8),(4,9),(4,12),(5,9),(5,11),(5,12),(6,8),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14)],15)
=> ? = 2
[1,3,5,4,2] => [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,6),(0,9),(1,3),(1,4),(1,5),(2,3),(2,4),(2,9),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[1,4,2,3,5] => [2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2
[1,4,2,5,3] => [2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? = 2
[1,4,3,2,5] => [2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[1,4,3,5,2] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[1,4,5,2,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? = 2
[1,4,5,3,2] => [2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? = 2
[1,5,2,3,4] => [2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2
[1,5,2,4,3] => [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? = 2
[1,5,3,2,4] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? = 2
[1,5,3,4,2] => [2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? = 2
[1,5,4,2,3] => [2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2
[1,5,4,3,2] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? = 2
[2,1,3,4,5] => [3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2
[2,1,3,5,4] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2
[2,1,4,3,5] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? = 2
[2,1,4,5,3] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 2
[2,1,5,3,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2
[2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? = 2
[2,3,1,4,5] => [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2
[2,3,1,5,4] => [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2
[2,3,4,1,5] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[2,3,5,1,4] => [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2
[2,3,5,4,1] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 2
[2,4,1,3,5] => [4,2,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? = 2
[2,4,1,5,3] => [4,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2
[2,4,3,1,5] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? = 2
[2,4,3,5,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[2,4,5,1,3] => [5,2,1,3,4] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2
[2,4,5,3,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[2,5,1,3,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? = 2
[2,5,1,4,3] => [4,2,1,5,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2
[2,5,3,1,4] => [5,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? = 2
[2,5,3,4,1] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2
[2,5,4,1,3] => [5,2,1,4,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? = 2
[2,5,4,3,1] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 2
[3,1,2,4,5] => [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2
[4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 2
[5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 2
Description
The induced matching number of a graph.
An induced matching of a graph is a set of independent edges which is an induced subgraph. This statistic records the maximal number of edges in an induced matching.
Matching statistic: St001261
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001261: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Mp00209: Permutations —pattern poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001261: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Values
[1] => [1] => ([],1)
=> ([],1)
=> 1 = 0 + 1
[1,2] => [2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 1 + 1
[2,1] => [1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 1 + 1
[1,2,3] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
[1,3,2] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
[2,1,3] => [3,2,1] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 2 = 1 + 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 2 = 1 + 1
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
[3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
[1,2,3,4] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[1,2,4,3] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[1,3,2,4] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[1,3,4,2] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[1,4,2,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? = 2 + 1
[1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 2 = 1 + 1
[2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[2,1,4,3] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[2,3,1,4] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2 = 1 + 1
[2,4,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[3,1,2,4] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[3,1,4,2] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2 = 1 + 1
[3,2,4,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[3,4,1,2] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[3,4,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[4,1,2,3] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 2 = 1 + 1
[4,1,3,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? = 2 + 1
[4,2,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[4,2,3,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[4,3,1,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 3 = 2 + 1
[4,3,2,1] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 2 + 1
[1,2,3,4,5] => [2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 2 + 1
[1,2,3,5,4] => [2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[1,2,4,3,5] => [2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2 + 1
[1,2,4,5,3] => [2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[1,2,5,3,4] => [2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? = 2 + 1
[1,2,5,4,3] => [2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? = 2 + 1
[1,3,2,4,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2 + 1
[1,3,2,5,4] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2 + 1
[1,3,4,2,5] => [2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2 + 1
[1,3,4,5,2] => [2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 2 + 1
[1,3,5,2,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(0,13),(0,14),(1,5),(1,6),(1,14),(2,3),(2,4),(2,13),(3,10),(3,11),(3,12),(4,8),(4,9),(4,12),(5,9),(5,11),(5,12),(6,8),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14)],15)
=> ? = 2 + 1
[1,3,5,4,2] => [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,6),(0,9),(1,3),(1,4),(1,5),(2,3),(2,4),(2,9),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[1,4,2,3,5] => [2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2 + 1
[1,4,2,5,3] => [2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? = 2 + 1
[1,4,3,2,5] => [2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[1,4,3,5,2] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[1,4,5,2,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? = 2 + 1
[1,4,5,3,2] => [2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? = 2 + 1
[1,5,2,3,4] => [2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2 + 1
[1,5,2,4,3] => [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? = 2 + 1
[1,5,3,2,4] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? = 2 + 1
[1,5,3,4,2] => [2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? = 2 + 1
[1,5,4,2,3] => [2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2 + 1
[1,5,4,3,2] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? = 2 + 1
[2,1,3,4,5] => [3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2 + 1
[2,1,3,5,4] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2 + 1
[2,1,4,3,5] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? = 2 + 1
[2,1,4,5,3] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 2 + 1
[2,1,5,3,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2 + 1
[2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? = 2 + 1
[2,3,1,4,5] => [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2 + 1
[2,3,1,5,4] => [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2 + 1
[2,3,4,1,5] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 3 = 2 + 1
[2,3,5,1,4] => [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? = 2 + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 2 + 1
[2,4,1,3,5] => [4,2,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? = 2 + 1
[2,4,1,5,3] => [4,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2 + 1
[2,4,3,1,5] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? = 2 + 1
[2,4,3,5,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[2,4,5,1,3] => [5,2,1,3,4] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? = 2 + 1
[2,4,5,3,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[2,5,1,3,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? = 2 + 1
[2,5,1,4,3] => [4,2,1,5,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? = 2 + 1
[2,5,3,1,4] => [5,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? = 2 + 1
[2,5,3,4,1] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 2 + 1
[2,5,4,1,3] => [5,2,1,4,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? = 2 + 1
[2,5,4,3,1] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? = 2 + 1
[3,1,2,4,5] => [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? = 2 + 1
[4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 3 = 2 + 1
[2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 3 = 2 + 1
[5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 3 = 2 + 1
Description
The Castelnuovo-Mumford regularity of a graph.
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