Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000401
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Mapping
St000401: 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] => 2
[1,3,2] => 4
[2,1,3] => 4
[2,3,1] => 4
[3,1,2] => 4
[3,2,1] => 2
[1,2,3,4] => 2
[1,2,4,3] => 4
[1,3,2,4] => 2
[1,3,4,2] => 8
[1,4,2,3] => 8
[1,4,3,2] => 4
[2,1,3,4] => 4
[2,1,4,3] => 2
[2,3,1,4] => 8
[2,3,4,1] => 4
[2,4,1,3] => 2
[2,4,3,1] => 8
[3,1,2,4] => 8
[3,1,4,2] => 2
[3,2,1,4] => 4
[3,2,4,1] => 8
[3,4,1,2] => 2
[3,4,2,1] => 4
[4,1,2,3] => 4
[4,1,3,2] => 8
[4,2,1,3] => 8
[4,2,3,1] => 2
[4,3,1,2] => 4
[4,3,2,1] => 2
[1,2,3,4,5] => 2
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 8
[1,2,5,3,4] => 8
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 8
[1,3,5,2,4] => 8
[1,3,5,4,2] => 8
[1,4,2,3,5] => 4
[1,4,2,5,3] => 8
[1,4,3,2,5] => 2
[1,4,3,5,2] => 8
[1,4,5,2,3] => 4
Description
The size of the symmetry class of a permutation. The symmetry class of a permutation $\pi$ is the set of all permutations that can be obtained from $\pi$ by the three elementary operations '''inverse''' ([[Mp00066]]), '''reverse''' ([[Mp00064]]), and '''complement''' ([[Mp00069]]). Two elements in the same symmetry class are also in the same Wilf-equivalence class, see for example [2].