Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000811
Mapping
St000811: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 0
[1,1]
 => 2
[3]
 => 1
[2,1]
 => 0
[1,1,1]
 => 4
[4]
 => 0
[3,1]
 => 1
[2,2]
 => 2
[2,1,1]
 => 0
[1,1,1,1]
 => 10
[5]
 => 1
[4,1]
 => 0
[3,2]
 => 0
[3,1,1]
 => 2
[2,2,1]
 => 2
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 26
[6]
 => 0
[5,1]
 => 1
[4,2]
 => 0
[4,1,1]
 => 0
[3,3]
 => 4
[3,2,1]
 => 0
[3,1,1,1]
 => 4
[2,2,2]
 => 0
[2,2,1,1]
 => 4
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 76
[7]
 => 1
[6,1]
 => 0
[5,2]
 => 0
[5,1,1]
 => 2
[4,3]
 => 0
[4,2,1]
 => 0
[4,1,1,1]
 => 0
[3,3,1]
 => 4
[3,2,2]
 => 2
[3,2,1,1]
 => 0
[3,1,1,1,1]
 => 10
[2,2,2,1]
 => 0
[2,2,1,1,1]
 => 8
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 232
[8]
 => 0
[7,1]
 => 1
[6,2]
 => 0
[6,1,1]
 => 0
[5,3]
 => 1
[5,2,1]
 => 0
Description
The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. For example, $p_{22} = s_{1111} - s_{211} + 2s_{22} - s_{31} + s_4$, so the statistic on the partition $22$ is 2. This is also the sum of the character values at the given conjugacy class over all irreducible characters of the symmetric group. [2] For a permutation $\pi$ of given cycle type, this is also the number of permutations whose square equals $\pi$. [2]