Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000458
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Mapping
St000458: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 3
[3,1,2] => 3
[3,2,1] => 3
[1,2,3,4] => 5
[1,2,4,3] => 5
[1,3,2,4] => 5
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 5
[2,1,4,3] => 5
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 1
[2,4,3,1] => 3
[3,1,2,4] => 3
[3,1,4,2] => 1
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 5
[3,4,2,1] => 5
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 5
[4,3,1,2] => 5
[4,3,2,1] => 5
[1,2,3,4,5] => 8
[1,2,3,5,4] => 8
[1,2,4,3,5] => 8
[1,2,4,5,3] => 6
[1,2,5,3,4] => 6
[1,2,5,4,3] => 6
[1,3,2,4,5] => 8
[1,3,2,5,4] => 8
[1,3,4,2,5] => 3
[1,3,4,5,2] => 3
[1,3,5,2,4] => 1
[1,3,5,4,2] => 3
[1,4,2,3,5] => 3
[1,4,2,5,3] => 1
[1,4,3,2,5] => 3
[1,4,3,5,2] => 3
[1,4,5,2,3] => 5
Description
The number of permutations obtained by switching adjacencies or successions. For a permutation $\pi$, this statistic is the size of its equivalence class of the equivalence relation generated by the interchange of any two adjacent elements $\pi_i$ and $\pi_{i+1}$ such that $|\pi_i - \pi_{i+1}| = 1$.