Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001710
Mapping
St001710: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 2
[3]
 => 1
[2,1]
 => 4
[1,1,1]
 => 4
[4]
 => 2
[3,1]
 => 1
[2,2]
 => 10
[2,1,1]
 => 10
[1,1,1,1]
 => 10
[5]
 => 1
[4,1]
 => 2
[3,2]
 => 2
[3,1,1]
 => 2
[2,2,1]
 => 26
[2,1,1,1]
 => 26
[1,1,1,1,1]
 => 26
[6]
 => 4
[5,1]
 => 1
[4,2]
 => 4
[4,1,1]
 => 4
[3,3]
 => 4
[3,2,1]
 => 4
[3,1,1,1]
 => 4
[2,2,2]
 => 76
[2,2,1,1]
 => 76
[2,1,1,1,1]
 => 76
[1,1,1,1,1,1]
 => 76
[7]
 => 1
[6,1]
 => 4
[5,2]
 => 2
[5,1,1]
 => 2
[4,3]
 => 2
[4,2,1]
 => 8
[4,1,1,1]
 => 8
[3,3,1]
 => 4
[3,2,2]
 => 10
[3,2,1,1]
 => 10
[3,1,1,1,1]
 => 10
[2,2,2,1]
 => 232
[2,2,1,1,1]
 => 232
[2,1,1,1,1,1]
 => 232
[1,1,1,1,1,1,1]
 => 232
[8]
 => 4
[7,1]
 => 1
[6,2]
 => 8
[6,1,1]
 => 8
[5,3]
 => 1
[5,2,1]
 => 4
Description
The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. Let $\alpha$ be any permutation of cycle type $\lambda$. This statistic is the number of permutations $\pi$ such that $$ \alpha\pi\alpha^{-1} = \pi^{-1}.$$