Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000567
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00323: Integer partitions —Loehr-Warrington inverse⟶ Integer partitions
St000567: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-1,-2] => [1,1]
 => [2]
 => 0
[2,-1] => [2]
 => [1,1]
 => 1
[-2,1] => [2]
 => [1,1]
 => 1
[1,-2,-3] => [1,1]
 => [2]
 => 0
[-1,2,-3] => [1,1]
 => [2]
 => 0
[-1,-2,3] => [1,1]
 => [2]
 => 0
[-1,-2,-3] => [1,1,1]
 => [3]
 => 0
[1,3,-2] => [2]
 => [1,1]
 => 1
[1,-3,2] => [2]
 => [1,1]
 => 1
[-1,3,-2] => [2,1]
 => [1,1,1]
 => 3
[-1,-3,2] => [2,1]
 => [1,1,1]
 => 3
[2,-1,3] => [2]
 => [1,1]
 => 1
[2,-1,-3] => [2,1]
 => [1,1,1]
 => 3
[-2,1,3] => [2]
 => [1,1]
 => 1
[-2,1,-3] => [2,1]
 => [1,1,1]
 => 3
[2,3,-1] => [3]
 => [2,1]
 => 2
[2,-3,1] => [3]
 => [2,1]
 => 2
[-2,3,1] => [3]
 => [2,1]
 => 2
[-2,-3,-1] => [3]
 => [2,1]
 => 2
[3,1,-2] => [3]
 => [2,1]
 => 2
[3,-1,2] => [3]
 => [2,1]
 => 2
[-3,1,2] => [3]
 => [2,1]
 => 2
[-3,-1,-2] => [3]
 => [2,1]
 => 2
[3,2,-1] => [2]
 => [1,1]
 => 1
[3,-2,-1] => [2,1]
 => [1,1,1]
 => 3
[-3,2,1] => [2]
 => [1,1]
 => 1
[-3,-2,1] => [2,1]
 => [1,1,1]
 => 3
[1,2,-3,-4] => [1,1]
 => [2]
 => 0
[1,-2,3,-4] => [1,1]
 => [2]
 => 0
[1,-2,-3,4] => [1,1]
 => [2]
 => 0
[1,-2,-3,-4] => [1,1,1]
 => [3]
 => 0
[-1,2,3,-4] => [1,1]
 => [2]
 => 0
[-1,2,-3,4] => [1,1]
 => [2]
 => 0
[-1,2,-3,-4] => [1,1,1]
 => [3]
 => 0
[-1,-2,3,4] => [1,1]
 => [2]
 => 0
[-1,-2,3,-4] => [1,1,1]
 => [3]
 => 0
[-1,-2,-3,4] => [1,1,1]
 => [3]
 => 0
[-1,-2,-3,-4] => [1,1,1,1]
 => [4]
 => 0
[1,2,4,-3] => [2]
 => [1,1]
 => 1
[1,2,-4,3] => [2]
 => [1,1]
 => 1
[1,-2,4,-3] => [2,1]
 => [1,1,1]
 => 3
[1,-2,-4,3] => [2,1]
 => [1,1,1]
 => 3
[-1,2,4,-3] => [2,1]
 => [1,1,1]
 => 3
[-1,2,-4,3] => [2,1]
 => [1,1,1]
 => 3
[-1,-2,4,3] => [1,1]
 => [2]
 => 0
[-1,-2,4,-3] => [2,1,1]
 => [3,1]
 => 3
[-1,-2,-4,3] => [2,1,1]
 => [3,1]
 => 3
[-1,-2,-4,-3] => [1,1]
 => [2]
 => 0
[1,3,-2,4] => [2]
 => [1,1]
 => 1
[1,3,-2,-4] => [2,1]
 => [1,1,1]
 => 3
Description
The sum of the products of all pairs of parts. This is the evaluation of the second elementary symmetric polynomial which is equal to $$e_2(\lambda) = \binom{n+1}{2} - \sum_{i=1}^\ell\binom{\lambda_i+1}{2}$$ for a partition $\lambda = (\lambda_1,\dots,\lambda_\ell) \vdash n$, see [1]. This is the maximal number of inversions a permutation with the given shape can have, see [2, cor.2.4].
Matching statistic: St001541
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00323: Integer partitions —Loehr-Warrington inverse⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001541: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-1,-2] => [1,1]
 => [2]
 => [1,1]
 => 0
[2,-1] => [2]
 => [1,1]
 => [2]
 => 1
[-2,1] => [2]
 => [1,1]
 => [2]
 => 1
[1,-2,-3] => [1,1]
 => [2]
 => [1,1]
 => 0
[-1,2,-3] => [1,1]
 => [2]
 => [1,1]
 => 0
[-1,-2,3] => [1,1]
 => [2]
 => [1,1]
 => 0
[-1,-2,-3] => [1,1,1]
 => [3]
 => [1,1,1]
 => 0
[1,3,-2] => [2]
 => [1,1]
 => [2]
 => 1
[1,-3,2] => [2]
 => [1,1]
 => [2]
 => 1
[-1,3,-2] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[-1,-3,2] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[2,-1,3] => [2]
 => [1,1]
 => [2]
 => 1
[2,-1,-3] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[-2,1,3] => [2]
 => [1,1]
 => [2]
 => 1
[-2,1,-3] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[2,3,-1] => [3]
 => [2,1]
 => [2,1]
 => 2
[2,-3,1] => [3]
 => [2,1]
 => [2,1]
 => 2
[-2,3,1] => [3]
 => [2,1]
 => [2,1]
 => 2
[-2,-3,-1] => [3]
 => [2,1]
 => [2,1]
 => 2
[3,1,-2] => [3]
 => [2,1]
 => [2,1]
 => 2
[3,-1,2] => [3]
 => [2,1]
 => [2,1]
 => 2
[-3,1,2] => [3]
 => [2,1]
 => [2,1]
 => 2
[-3,-1,-2] => [3]
 => [2,1]
 => [2,1]
 => 2
[3,2,-1] => [2]
 => [1,1]
 => [2]
 => 1
[3,-2,-1] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[-3,2,1] => [2]
 => [1,1]
 => [2]
 => 1
[-3,-2,1] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[1,2,-3,-4] => [1,1]
 => [2]
 => [1,1]
 => 0
[1,-2,3,-4] => [1,1]
 => [2]
 => [1,1]
 => 0
[1,-2,-3,4] => [1,1]
 => [2]
 => [1,1]
 => 0
[1,-2,-3,-4] => [1,1,1]
 => [3]
 => [1,1,1]
 => 0
[-1,2,3,-4] => [1,1]
 => [2]
 => [1,1]
 => 0
[-1,2,-3,4] => [1,1]
 => [2]
 => [1,1]
 => 0
[-1,2,-3,-4] => [1,1,1]
 => [3]
 => [1,1,1]
 => 0
[-1,-2,3,4] => [1,1]
 => [2]
 => [1,1]
 => 0
[-1,-2,3,-4] => [1,1,1]
 => [3]
 => [1,1,1]
 => 0
[-1,-2,-3,4] => [1,1,1]
 => [3]
 => [1,1,1]
 => 0
[-1,-2,-3,-4] => [1,1,1,1]
 => [4]
 => [1,1,1,1]
 => 0
[1,2,4,-3] => [2]
 => [1,1]
 => [2]
 => 1
[1,2,-4,3] => [2]
 => [1,1]
 => [2]
 => 1
[1,-2,4,-3] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[1,-2,-4,3] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[-1,2,4,-3] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[-1,2,-4,3] => [2,1]
 => [1,1,1]
 => [3]
 => 3
[-1,-2,4,3] => [1,1]
 => [2]
 => [1,1]
 => 0
[-1,-2,4,-3] => [2,1,1]
 => [3,1]
 => [2,1,1]
 => 3
[-1,-2,-4,3] => [2,1,1]
 => [3,1]
 => [2,1,1]
 => 3
[-1,-2,-4,-3] => [1,1]
 => [2]
 => [1,1]
 => 0
[1,3,-2,4] => [2]
 => [1,1]
 => [2]
 => 1
[1,3,-2,-4] => [2,1]
 => [1,1,1]
 => [3]
 => 3
Description
The Gini index of an integer partition. As discussed in [1], this statistic is equal to [[St000567]] applied to the conjugate partition.