Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000937
Mapping
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000937: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,3,2] => [2,1]
 => [1,1,1]
 => [1,1]
 => 1
[2,1,3] => [2,1]
 => [1,1,1]
 => [1,1]
 => 1
[3,2,1] => [2,1]
 => [1,1,1]
 => [1,1]
 => 1
[1,2,3,4] => [1,1,1,1]
 => [2,2]
 => [2]
 => 2
[1,2,4,3] => [2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[1,3,2,4] => [2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[1,4,3,2] => [2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[2,1,3,4] => [2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[2,3,4,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[2,4,1,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[3,1,4,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[3,2,1,4] => [2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[3,4,2,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[4,1,2,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[4,2,3,1] => [2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[4,3,1,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[1,2,3,4,5] => [1,1,1,1,1]
 => [2,2,1]
 => [2,1]
 => 1
[1,2,3,5,4] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[1,2,4,3,5] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[1,2,4,5,3] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,2,5,3,4] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,2,5,4,3] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[1,3,2,4,5] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[1,3,4,2,5] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,3,4,5,2] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,3,5,2,4] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,3,5,4,2] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,4,2,3,5] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,4,2,5,3] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,4,3,2,5] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[1,4,3,5,2] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,4,5,3,2] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,5,2,3,4] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,5,2,4,3] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,5,3,2,4] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[1,5,3,4,2] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[1,5,4,2,3] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[2,1,3,4,5] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[2,1,4,5,3] => [3,2]
 => [3,1,1]
 => [1,1]
 => 1
[2,1,5,3,4] => [3,2]
 => [3,1,1]
 => [1,1]
 => 1
[2,3,1,4,5] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[2,3,1,5,4] => [3,2]
 => [3,1,1]
 => [1,1]
 => 1
[2,3,4,1,5] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[2,3,5,4,1] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[2,4,1,3,5] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[2,4,3,1,5] => [3,1,1]
 => [3,2]
 => [2]
 => 2
[2,4,3,5,1] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[2,4,5,1,3] => [3,2]
 => [3,1,1]
 => [1,1]
 => 1
[2,5,1,4,3] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[2,5,3,1,4] => [4,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
Description
The number of positive values of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation $S^{(2,2)}$ are $2$ on the conjugacy classes $(4)$ and $(2,2)$, $0$ on the conjugacy classes $(3,1)$ and $(1,1,1,1)$, and $-1$ on the conjugacy class $(2,1,1)$. Therefore, the statistic on the partition $(2,2)$ is $2$.