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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001528
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Mapping
St001528: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 1
[1,2,4,3] => 6
[1,3,2,4] => 6
[1,3,4,2] => 8
[1,4,2,3] => 8
[1,4,3,2] => 6
[2,1,3,4] => 6
[2,1,4,3] => 9
[2,3,1,4] => 8
[2,3,4,1] => 9
[2,4,1,3] => 9
[2,4,3,1] => 8
[3,1,2,4] => 8
[3,1,4,2] => 9
[3,2,1,4] => 6
[3,2,4,1] => 8
[3,4,1,2] => 9
[3,4,2,1] => 9
[4,1,2,3] => 9
[4,1,3,2] => 8
[4,2,1,3] => 8
[4,2,3,1] => 6
[4,3,1,2] => 9
[4,3,2,1] => 9
[1,2,3,4,5] => 1
[1,2,3,5,4] => 10
[1,2,4,3,5] => 10
[1,2,4,5,3] => 20
[1,2,5,3,4] => 20
[1,2,5,4,3] => 10
[1,3,2,4,5] => 10
[1,3,2,5,4] => 45
[1,3,4,2,5] => 20
[1,3,4,5,2] => 45
[1,3,5,2,4] => 45
[1,3,5,4,2] => 20
[1,4,2,3,5] => 20
[1,4,2,5,3] => 45
[1,4,3,2,5] => 10
[1,4,3,5,2] => 20
[1,4,5,2,3] => 45
Description
The number of permutations such that the product with the permutation has the same number of fixed points. More formally, given a permutation π, this is the number of permutations σ such that π and πσ have the same number of fixed points. Note that the number of permutations σ such that π and πσ have the same cycle type is the size of the conjugacy class of π, [[St000690]].