Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000690
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Mapping
St000690: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[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] => 3
[2,3,1,4] => 8
[2,3,4,1] => 6
[2,4,1,3] => 6
[2,4,3,1] => 8
[3,1,2,4] => 8
[3,1,4,2] => 6
[3,2,1,4] => 6
[3,2,4,1] => 8
[3,4,1,2] => 3
[3,4,2,1] => 6
[4,1,2,3] => 6
[4,1,3,2] => 8
[4,2,1,3] => 8
[4,2,3,1] => 6
[4,3,1,2] => 6
[4,3,2,1] => 3
[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] => 15
[1,3,4,2,5] => 20
[1,3,4,5,2] => 30
[1,3,5,2,4] => 30
[1,3,5,4,2] => 20
[1,4,2,3,5] => 20
[1,4,2,5,3] => 30
[1,4,3,2,5] => 10
[1,4,3,5,2] => 20
[1,4,5,2,3] => 15
[1,4,5,3,2] => 30
Description
The size of the conjugacy class of a permutation. Two permutations are conjugate if and only if they have the same cycle type, this statistic is then computed as described in [[St000182]].
Matching statistic: St000182
Mapping
Mp00108: Permutations —cycle type⟶ Integer partitions
St000182: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,1]
 => 1
[2,1] => [2]
 => 1
[1,2,3] => [1,1,1]
 => 1
[1,3,2] => [2,1]
 => 3
[2,1,3] => [2,1]
 => 3
[2,3,1] => [3]
 => 2
[3,1,2] => [3]
 => 2
[3,2,1] => [2,1]
 => 3
[1,2,3,4] => [1,1,1,1]
 => 1
[1,2,4,3] => [2,1,1]
 => 6
[1,3,2,4] => [2,1,1]
 => 6
[1,3,4,2] => [3,1]
 => 8
[1,4,2,3] => [3,1]
 => 8
[1,4,3,2] => [2,1,1]
 => 6
[2,1,3,4] => [2,1,1]
 => 6
[2,1,4,3] => [2,2]
 => 3
[2,3,1,4] => [3,1]
 => 8
[2,3,4,1] => [4]
 => 6
[2,4,1,3] => [4]
 => 6
[2,4,3,1] => [3,1]
 => 8
[3,1,2,4] => [3,1]
 => 8
[3,1,4,2] => [4]
 => 6
[3,2,1,4] => [2,1,1]
 => 6
[3,2,4,1] => [3,1]
 => 8
[3,4,1,2] => [2,2]
 => 3
[3,4,2,1] => [4]
 => 6
[4,1,2,3] => [4]
 => 6
[4,1,3,2] => [3,1]
 => 8
[4,2,1,3] => [3,1]
 => 8
[4,2,3,1] => [2,1,1]
 => 6
[4,3,1,2] => [4]
 => 6
[4,3,2,1] => [2,2]
 => 3
[1,2,3,4,5] => [1,1,1,1,1]
 => 1
[1,2,3,5,4] => [2,1,1,1]
 => 10
[1,2,4,3,5] => [2,1,1,1]
 => 10
[1,2,4,5,3] => [3,1,1]
 => 20
[1,2,5,3,4] => [3,1,1]
 => 20
[1,2,5,4,3] => [2,1,1,1]
 => 10
[1,3,2,4,5] => [2,1,1,1]
 => 10
[1,3,2,5,4] => [2,2,1]
 => 15
[1,3,4,2,5] => [3,1,1]
 => 20
[1,3,4,5,2] => [4,1]
 => 30
[1,3,5,2,4] => [4,1]
 => 30
[1,3,5,4,2] => [3,1,1]
 => 20
[1,4,2,3,5] => [3,1,1]
 => 20
[1,4,2,5,3] => [4,1]
 => 30
[1,4,3,2,5] => [2,1,1,1]
 => 10
[1,4,3,5,2] => [3,1,1]
 => 20
[1,4,5,2,3] => [2,2,1]
 => 15
[1,4,5,3,2] => [4,1]
 => 30
Description
The number of permutations whose cycle type is the given integer partition. This number is given by $$\{ \pi \in \mathfrak{S}_n : \text{type}(\pi) = \lambda\} = \frac{n!}{\lambda_1 \cdots \lambda_k \mu_1(\lambda)! \cdots \mu_n(\lambda)!}$$ where $\mu_j(\lambda)$ denotes the number of parts of $\lambda$ equal to $j$. All permutations with the same cycle type form a [[wikipedia:Conjugacy class]].