Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001434
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Mapping
St001434: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[-1] => 0
[1,2] => 0
[1,-2] => 1
[-1,2] => 0
[-1,-2] => 1
[2,1] => 0
[2,-1] => 0
[-2,1] => 1
[-2,-1] => 1
[1,2,3] => 0
[1,2,-3] => 2
[1,-2,3] => 1
[1,-2,-3] => 3
[-1,2,3] => 0
[-1,2,-3] => 2
[-1,-2,3] => 1
[-1,-2,-3] => 3
[1,3,2] => 0
[1,3,-2] => 1
[1,-3,2] => 2
[1,-3,-2] => 3
[-1,3,2] => 0
[-1,3,-2] => 1
[-1,-3,2] => 2
[-1,-3,-2] => 3
[2,1,3] => 0
[2,1,-3] => 2
[2,-1,3] => 0
[2,-1,-3] => 2
[-2,1,3] => 1
[-2,1,-3] => 3
[-2,-1,3] => 1
[-2,-1,-3] => 3
[2,3,1] => 0
[2,3,-1] => 0
[2,-3,1] => 2
[2,-3,-1] => 2
[-2,3,1] => 1
[-2,3,-1] => 1
[-2,-3,1] => 3
[-2,-3,-1] => 3
[3,1,2] => 0
[3,1,-2] => 1
[3,-1,2] => 0
[3,-1,-2] => 1
[-3,1,2] => 2
[-3,1,-2] => 3
[-3,-1,2] => 2
[-3,-1,-2] => 3
Description
The number of negative sum pairs of a signed permutation. The number of negative sum pairs of a signed permutation $\sigma$ is: $$\operatorname{nsp}(\sigma)=\big|\{1\leq i < j\leq n \mid \sigma(i)+\sigma(j) < 0\}\big|,$$ see [1, Eq.(8.1)].
Matching statistic: St001604
Mapping
Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 14%
Values
[1] => [1] => [1]
 => []
 => ? = 0
[-1] => [-1] => []
 => ?
 => ? = 0
[1,2] => [2,1] => [2]
 => []
 => ? = 0
[1,-2] => [-2,1] => []
 => ?
 => ? = 1
[-1,2] => [2,-1] => []
 => ?
 => ? = 0
[-1,-2] => [-2,-1] => [2]
 => []
 => ? = 1
[2,1] => [1,2] => [1,1]
 => [1]
 => ? = 0
[2,-1] => [-1,2] => [1]
 => []
 => ? = 0
[-2,1] => [1,-2] => [1]
 => []
 => ? = 1
[-2,-1] => [-1,-2] => []
 => ?
 => ? = 1
[1,2,3] => [3,2,1] => [2,1]
 => [1]
 => ? = 0
[1,2,-3] => [-3,2,1] => [1]
 => []
 => ? = 2
[1,-2,3] => [3,-2,1] => [2]
 => []
 => ? = 1
[1,-2,-3] => [-3,-2,1] => []
 => ?
 => ? = 3
[-1,2,3] => [3,2,-1] => [1]
 => []
 => ? = 0
[-1,2,-3] => [-3,2,-1] => [2,1]
 => [1]
 => ? = 2
[-1,-2,3] => [3,-2,-1] => []
 => ?
 => ? = 1
[-1,-2,-3] => [-3,-2,-1] => [2]
 => []
 => ? = 3
[1,3,2] => [2,3,1] => [3]
 => []
 => ? = 0
[1,3,-2] => [-2,3,1] => []
 => ?
 => ? = 1
[1,-3,2] => [2,-3,1] => []
 => ?
 => ? = 2
[1,-3,-2] => [-2,-3,1] => [3]
 => []
 => ? = 3
[-1,3,2] => [2,3,-1] => []
 => ?
 => ? = 0
[-1,3,-2] => [-2,3,-1] => [3]
 => []
 => ? = 1
[-1,-3,2] => [2,-3,-1] => [3]
 => []
 => ? = 2
[-1,-3,-2] => [-2,-3,-1] => []
 => ?
 => ? = 3
[2,1,3] => [3,1,2] => [3]
 => []
 => ? = 0
[2,1,-3] => [-3,1,2] => []
 => ?
 => ? = 2
[2,-1,3] => [3,-1,2] => []
 => ?
 => ? = 0
[2,-1,-3] => [-3,-1,2] => [3]
 => []
 => ? = 2
[-2,1,3] => [3,1,-2] => []
 => ?
 => ? = 1
[-2,1,-3] => [-3,1,-2] => [3]
 => []
 => ? = 3
[-2,-1,3] => [3,-1,-2] => [3]
 => []
 => ? = 1
[-2,-1,-3] => [-3,-1,-2] => []
 => ?
 => ? = 3
[2,3,1] => [1,3,2] => [2,1]
 => [1]
 => ? = 0
[2,3,-1] => [-1,3,2] => [2]
 => []
 => ? = 0
[2,-3,1] => [1,-3,2] => [1]
 => []
 => ? = 2
[2,-3,-1] => [-1,-3,2] => []
 => ?
 => ? = 2
[-2,3,1] => [1,3,-2] => [1]
 => []
 => ? = 1
[-2,3,-1] => [-1,3,-2] => []
 => ?
 => ? = 1
[-2,-3,1] => [1,-3,-2] => [2,1]
 => [1]
 => ? = 3
[-2,-3,-1] => [-1,-3,-2] => [2]
 => []
 => ? = 3
[3,1,2] => [2,1,3] => [2,1]
 => [1]
 => ? = 0
[3,1,-2] => [-2,1,3] => [1]
 => []
 => ? = 1
[3,-1,2] => [2,-1,3] => [1]
 => []
 => ? = 0
[3,-1,-2] => [-2,-1,3] => [2,1]
 => [1]
 => ? = 1
[-3,1,2] => [2,1,-3] => [2]
 => []
 => ? = 2
[-3,1,-2] => [-2,1,-3] => []
 => ?
 => ? = 3
[-3,-1,2] => [2,-1,-3] => []
 => ?
 => ? = 2
[-3,-1,-2] => [-2,-1,-3] => [2]
 => []
 => ? = 3
[4,3,2,1] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,2,3,4,5] => [5,4,3,2,1] => [2,2,1]
 => [2,1]
 => 0
[1,3,4,2,5] => [5,2,4,3,1] => [2,2,1]
 => [2,1]
 => 0
[1,4,2,3,5] => [5,3,2,4,1] => [2,2,1]
 => [2,1]
 => 0
[1,4,3,2,5] => [5,2,3,4,1] => [2,1,1,1]
 => [1,1,1]
 => 0
[2,1,3,5,4] => [4,5,3,1,2] => [2,2,1]
 => [2,1]
 => 0
[2,3,4,5,1] => [1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 0
[2,4,1,5,3] => [3,5,1,4,2] => [2,2,1]
 => [2,1]
 => 0
[2,4,3,5,1] => [1,5,3,4,2] => [2,1,1,1]
 => [1,1,1]
 => 0
[3,1,5,2,4] => [4,2,5,1,3] => [2,2,1]
 => [2,1]
 => 0
[3,2,5,4,1] => [1,4,5,2,3] => [2,2,1]
 => [2,1]
 => 0
[3,4,5,1,2] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0
[3,4,5,2,1] => [1,2,5,4,3] => [2,1,1,1]
 => [1,1,1]
 => 0
[4,5,1,2,3] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0
[4,5,2,3,1] => [1,3,2,5,4] => [2,2,1]
 => [2,1]
 => 0
[4,5,3,1,2] => [2,1,3,5,4] => [2,2,1]
 => [2,1]
 => 0
[4,5,3,2,1] => [1,2,3,5,4] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,1,2,3,4] => [4,3,2,1,5] => [2,2,1]
 => [2,1]
 => 0
[5,1,3,2,4] => [4,2,3,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,2,1,4,3] => [3,4,1,2,5] => [2,2,1]
 => [2,1]
 => 0
[5,2,3,4,1] => [1,4,3,2,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,3,4,1,2] => [2,1,4,3,5] => [2,2,1]
 => [2,1]
 => 0
[5,3,4,2,1] => [1,2,4,3,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,4,1,2,3] => [3,2,1,4,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,4,2,3,1] => [1,3,2,4,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,4,3,1,2] => [2,1,3,4,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,4,3,2,1] => [1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0
[5,4,3,2,-1] => [-1,2,3,4,5] => [1,1,1,1]
 => [1,1,1]
 => 0
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.