Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000938
Mapping
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00194: Signed permutations —Foata-Han inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St000938: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,2] => [1,1]
 => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,1,1]
 => 0
[3,1,2] => [3,1,2] => [3,1,2] => [3]
 => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,1,1,1]
 => 0
[1,3,4,2] => [1,3,4,2] => [-4,-3,1,2] => [4]
 => 0
[1,4,2,3] => [1,4,2,3] => [4,1,2,3] => [4]
 => 0
[1,4,3,2] => [1,4,3,2] => [3,-4,1,2] => [2]
 => 0
[2,1,3,4] => [2,1,3,4] => [-2,1,3,4] => [1,1]
 => 0
[2,3,4,1] => [2,3,4,1] => [-4,-3,-2,1] => [2]
 => 0
[2,4,3,1] => [2,4,3,1] => [3,-4,-2,1] => [4]
 => 0
[3,1,2,4] => [3,1,2,4] => [3,1,2,4] => [3,1]
 => 1
[3,4,1,2] => [3,4,1,2] => [3,4,1,2] => [2,2]
 => 2
[3,4,2,1] => [3,4,2,1] => [2,4,-3,1] => [3]
 => 0
[4,2,1,3] => [4,2,1,3] => [-2,-4,1,3] => [4]
 => 0
[4,3,2,1] => [4,3,2,1] => [-3,2,-4,1] => [3,1]
 => 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1]
 => 0
[1,2,5,3,4] => [1,2,5,3,4] => [5,1,2,3,4] => [5]
 => 0
[1,3,2,4,5] => [1,3,2,4,5] => [-3,1,2,4,5] => [1,1]
 => 0
[1,3,2,5,4] => [1,3,2,5,4] => [-5,-3,1,2,4] => [5]
 => 0
[1,3,4,2,5] => [1,3,4,2,5] => [-4,-3,1,2,5] => [4,1]
 => 2
[1,3,4,5,2] => [1,3,4,5,2] => [-5,-4,-3,1,2] => [4]
 => 0
[1,3,5,2,4] => [1,3,5,2,4] => [3,-5,1,2,4] => [2]
 => 0
[1,3,5,4,2] => [1,3,5,4,2] => [4,-5,-3,1,2] => [2]
 => 0
[1,4,2,3,5] => [1,4,2,3,5] => [4,1,2,3,5] => [4,1]
 => 2
[1,4,2,5,3] => [1,4,2,5,3] => [5,-4,1,2,3] => [3]
 => 0
[1,4,3,2,5] => [1,4,3,2,5] => [3,-4,1,2,5] => [2,1]
 => 1
[1,4,5,2,3] => [1,4,5,2,3] => [4,5,1,2,3] => [5]
 => 0
[1,4,5,3,2] => [1,4,5,3,2] => [3,5,-4,1,2] => [2]
 => 0
[1,5,2,4,3] => [1,5,2,4,3] => [-4,-5,1,2,3] => [5]
 => 0
[1,5,4,2,3] => [1,5,4,2,3] => [-5,4,1,2,3] => [2]
 => 0
[2,1,3,4,5] => [2,1,3,4,5] => [-2,1,3,4,5] => [1,1,1]
 => 0
[2,1,5,4,3] => [2,1,5,4,3] => [4,-5,-2,1,3] => [3,2]
 => 1
[2,3,1,4,5] => [2,3,1,4,5] => [-3,-2,1,4,5] => [1,1]
 => 0
[2,3,1,5,4] => [2,3,1,5,4] => [-5,-3,-2,1,4] => [2]
 => 0
[2,3,4,1,5] => [2,3,4,1,5] => [-4,-3,-2,1,5] => [2,1]
 => 1
[2,3,4,5,1] => [2,3,4,5,1] => [-5,-4,-3,-2,1] => [2]
 => 0
[2,3,5,1,4] => [2,3,5,1,4] => [3,-5,-2,1,4] => [5]
 => 0
[2,3,5,4,1] => [2,3,5,4,1] => [4,-5,-3,-2,1] => [4]
 => 0
[2,4,1,5,3] => [2,4,1,5,3] => [2,-5,-4,1,3] => [5]
 => 0
[2,4,3,1,5] => [2,4,3,1,5] => [3,-4,-2,1,5] => [4,1]
 => 2
[2,4,5,3,1] => [2,4,5,3,1] => [3,5,-4,-2,1] => [5]
 => 0
[2,5,1,3,4] => [2,5,1,3,4] => [-2,-5,1,3,4] => [5]
 => 0
[2,5,1,4,3] => [2,5,1,4,3] => [2,4,-5,1,3] => [3]
 => 0
[3,1,2,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => [3,1,1]
 => 4
[3,1,5,2,4] => [3,1,5,2,4] => [3,5,1,2,4] => [3,2]
 => 1
[3,2,1,4,5] => [3,2,1,4,5] => [2,-3,1,4,5] => [1,1]
 => 0
[3,2,4,5,1] => [3,2,4,5,1] => [2,-5,-4,-3,1] => [2]
 => 0
[3,2,5,1,4] => [3,2,5,1,4] => [2,5,-3,1,4] => [4]
 => 0
[3,2,5,4,1] => [3,2,5,4,1] => [2,4,-5,-3,1] => [5]
 => 0
[3,4,1,2,5] => [3,4,1,2,5] => [3,4,1,2,5] => [2,2,1]
 => 1
Description
The number of zeros 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 $2$.