- FindStat

Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000938

Mapping

Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00194: Signed permutations —Foata-Han inverse⟶ Signed permutations
Mp00169: Signed permutations —odd 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] => [-1,-2] => [-1,-2] => [1,1]
 => 0
[2,1] => [2,1] => [-2,1] => [2]
 => 0
[-2,1] => [-2,-1] => [2,-1] => [2]
 => 0
[-2,-1] => [-1,-2] => [-1,-2] => [1,1]
 => 0
[1,-2,3] => [1,-2,-3] => [1,-2,-3] => [1,1]
 => 0
[1,-2,-3] => [1,-2,-3] => [1,-2,-3] => [1,1]
 => 0
[-1,2,3] => [-1,-2,3] => [-1,-2,3] => [1,1]
 => 0
[-1,2,-3] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[-1,-2,3] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[-1,-2,-3] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[1,3,2] => [1,3,2] => [-3,1,2] => [3]
 => 0
[1,-3,2] => [1,-3,-2] => [3,1,-2] => [3]
 => 0
[1,-3,-2] => [1,-2,-3] => [1,-2,-3] => [1,1]
 => 0
[-1,3,2] => [-1,-2,3] => [-1,-2,3] => [1,1]
 => 0
[-1,3,-2] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[-1,-3,2] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[-1,-3,-2] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[2,1,3] => [2,1,3] => [-2,1,3] => [2]
 => 0
[2,1,-3] => [2,1,-3] => [-2,1,-3] => [2,1]
 => 1
[2,-1,3] => [-1,2,-3] => [-1,2,-3] => [1,1]
 => 0
[2,-1,-3] => [-1,2,-3] => [-1,2,-3] => [1,1]
 => 0
[-2,1,3] => [-2,-1,3] => [2,-1,3] => [2]
 => 0
[-2,1,-3] => [-2,-1,-3] => [2,-1,-3] => [2,1]
 => 1
[-2,-1,3] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[-2,-1,-3] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[2,3,1] => [3,2,1] => [2,-3,1] => [3]
 => 0
[2,-3,1] => [-3,2,-1] => [-2,-3,-1] => [3]
 => 0
[2,-3,-1] => [-1,2,-3] => [-1,2,-3] => [1,1]
 => 0
[-2,3,1] => [-2,-1,3] => [2,-1,3] => [2]
 => 0
[-2,3,-1] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[-2,-3,1] => [-2,-1,-3] => [2,-1,-3] => [2,1]
 => 1
[-2,-3,-1] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[3,1,2] => [3,2,1] => [2,-3,1] => [3]
 => 0
[3,-1,2] => [-1,-2,3] => [-1,-2,3] => [1,1]
 => 0
[3,-1,-2] => [-1,-2,3] => [-1,-2,3] => [1,1]
 => 0
[-3,1,2] => [-3,2,-1] => [-2,-3,-1] => [3]
 => 0
[-3,-1,2] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[-3,-1,-2] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[3,2,1] => [3,2,1] => [2,-3,1] => [3]
 => 0
[3,-2,1] => [-2,-1,3] => [2,-1,3] => [2]
 => 0
[3,-2,-1] => [-1,-2,3] => [-1,-2,3] => [1,1]
 => 0
[-3,2,1] => [-3,2,-1] => [-2,-3,-1] => [3]
 => 0
[-3,-2,1] => [-2,-1,-3] => [2,-1,-3] => [2,1]
 => 1
[-3,-2,-1] => [-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => 0
[1,2,-3,4] => [1,2,-3,-4] => [1,2,-3,-4] => [1,1]
 => 0
[1,2,-3,-4] => [1,2,-3,-4] => [1,2,-3,-4] => [1,1]
 => 0
[1,-2,3,4] => [1,-2,-3,4] => [1,-2,-3,4] => [1,1]
 => 0
[1,-2,3,-4] => [1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
 => 0
[1,-2,-3,4] => [1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
 => 0

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

$2$ .

Matching statistic: St001604

Mapping

Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 25% ●values known / values provided: 39%●distinct values known / distinct values provided: 25%

Values

[-1,2] => [-1,-2] => [1,1]
 => [1]
 => ? = 0
[-1,-2] => [-1,-2] => [1,1]
 => [1]
 => ? = 0
[2,1] => [2,1] => []
 => ?
 => ? = 0
[-2,1] => [-2,-1] => []
 => ?
 => ? = 0
[-2,-1] => [-1,-2] => [1,1]
 => [1]
 => ? = 0
[1,-2,3] => [1,-2,-3] => [1,1]
 => [1]
 => ? = 0
[1,-2,-3] => [1,-2,-3] => [1,1]
 => [1]
 => ? = 0
[-1,2,3] => [-1,-2,3] => [1,1]
 => [1]
 => ? = 0
[-1,2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[-1,-2,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[1,3,2] => [1,3,2] => []
 => ?
 => ? = 0
[1,-3,2] => [1,-3,-2] => []
 => ?
 => ? = 0
[1,-3,-2] => [1,-2,-3] => [1,1]
 => [1]
 => ? = 0
[-1,3,2] => [-1,-2,3] => [1,1]
 => [1]
 => ? = 0
[-1,3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[-1,-3,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[-1,-3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[2,1,3] => [2,1,3] => []
 => ?
 => ? = 0
[2,1,-3] => [2,1,-3] => [1]
 => []
 => ? = 1
[2,-1,3] => [-1,2,-3] => [1,1]
 => [1]
 => ? = 0
[2,-1,-3] => [-1,2,-3] => [1,1]
 => [1]
 => ? = 0
[-2,1,3] => [-2,-1,3] => []
 => ?
 => ? = 0
[-2,1,-3] => [-2,-1,-3] => [1]
 => []
 => ? = 1
[-2,-1,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[-2,-1,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[2,3,1] => [3,2,1] => []
 => ?
 => ? = 0
[2,-3,1] => [-3,2,-1] => []
 => ?
 => ? = 0
[2,-3,-1] => [-1,2,-3] => [1,1]
 => [1]
 => ? = 0
[-2,3,1] => [-2,-1,3] => []
 => ?
 => ? = 0
[-2,3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[-2,-3,1] => [-2,-1,-3] => [1]
 => []
 => ? = 1
[-2,-3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[3,1,2] => [3,2,1] => []
 => ?
 => ? = 0
[3,-1,2] => [-1,-2,3] => [1,1]
 => [1]
 => ? = 0
[3,-1,-2] => [-1,-2,3] => [1,1]
 => [1]
 => ? = 0
[-3,1,2] => [-3,2,-1] => []
 => ?
 => ? = 0
[-3,-1,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[-3,-1,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[3,2,1] => [3,2,1] => []
 => ?
 => ? = 0
[3,-2,1] => [-2,-1,3] => []
 => ?
 => ? = 0
[3,-2,-1] => [-1,-2,3] => [1,1]
 => [1]
 => ? = 0
[-3,2,1] => [-3,2,-1] => []
 => ?
 => ? = 0
[-3,-2,1] => [-2,-1,-3] => [1]
 => []
 => ? = 1
[-3,-2,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 0
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
 => [1]
 => ? = 0
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
 => [1]
 => ? = 0
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
 => [1]
 => ? = 0
[1,-2,3,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 0
[1,-2,-3,4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 0
[-1,2,-3,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,2,-3,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,3,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,3,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,-3,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,-3,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,2,-4,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,4,3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,4,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,-4,3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,-4,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,3,-2,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,3,-2,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,2,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,2,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,-2,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,-2,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,3,-4,-2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,4,2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,4,-2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,-4,2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-3,-4,-2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,4,-2,3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,4,-2,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-4,2,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-4,-2,3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-4,-2,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,4,-3,2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,4,-3,-2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-4,3,-2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-4,-3,2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-4,-3,-2] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,3,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,3,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,-3,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,-3,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,4,3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,4,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,-4,3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-1,-4,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,3,-1,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,3,-1,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-3,-1,4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-3,-1,-4] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,3,-4,-1] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-3,4,-1] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-3,-4,-1] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,4,-1,3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,4,-1,-3] => [-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-2,-4,-1,3] => [-1,-2,-3,-4] => [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.

Matching statistic: St001603

Mapping

Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00194: Signed permutations —Foata-Han inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 25%

Values

[-1,2] => [-1,-2] => [-1,-2] => []
 => ? = 0 + 1
[-1,-2] => [-1,-2] => [-1,-2] => []
 => ? = 0 + 1
[2,1] => [2,1] => [-2,1] => []
 => ? = 0 + 1
[-2,1] => [-2,-1] => [2,-1] => []
 => ? = 0 + 1
[-2,-1] => [-1,-2] => [-1,-2] => []
 => ? = 0 + 1
[1,-2,3] => [1,-2,-3] => [1,-2,-3] => [1]
 => ? = 0 + 1
[1,-2,-3] => [1,-2,-3] => [1,-2,-3] => [1]
 => ? = 0 + 1
[-1,2,3] => [-1,-2,3] => [-1,-2,3] => [1]
 => ? = 0 + 1
[-1,2,-3] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[-1,-2,3] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[-1,-2,-3] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[1,3,2] => [1,3,2] => [-3,1,2] => []
 => ? = 0 + 1
[1,-3,2] => [1,-3,-2] => [3,1,-2] => []
 => ? = 0 + 1
[1,-3,-2] => [1,-2,-3] => [1,-2,-3] => [1]
 => ? = 0 + 1
[-1,3,2] => [-1,-2,3] => [-1,-2,3] => [1]
 => ? = 0 + 1
[-1,3,-2] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[-1,-3,2] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[-1,-3,-2] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[2,1,3] => [2,1,3] => [-2,1,3] => [1]
 => ? = 0 + 1
[2,1,-3] => [2,1,-3] => [-2,1,-3] => []
 => ? = 1 + 1
[2,-1,3] => [-1,2,-3] => [-1,2,-3] => [1]
 => ? = 0 + 1
[2,-1,-3] => [-1,2,-3] => [-1,2,-3] => [1]
 => ? = 0 + 1
[-2,1,3] => [-2,-1,3] => [2,-1,3] => [1]
 => ? = 0 + 1
[-2,1,-3] => [-2,-1,-3] => [2,-1,-3] => []
 => ? = 1 + 1
[-2,-1,3] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[-2,-1,-3] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[2,3,1] => [3,2,1] => [2,-3,1] => []
 => ? = 0 + 1
[2,-3,1] => [-3,2,-1] => [-2,-3,-1] => []
 => ? = 0 + 1
[2,-3,-1] => [-1,2,-3] => [-1,2,-3] => [1]
 => ? = 0 + 1
[-2,3,1] => [-2,-1,3] => [2,-1,3] => [1]
 => ? = 0 + 1
[-2,3,-1] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[-2,-3,1] => [-2,-1,-3] => [2,-1,-3] => []
 => ? = 1 + 1
[-2,-3,-1] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[3,1,2] => [3,2,1] => [2,-3,1] => []
 => ? = 0 + 1
[3,-1,2] => [-1,-2,3] => [-1,-2,3] => [1]
 => ? = 0 + 1
[3,-1,-2] => [-1,-2,3] => [-1,-2,3] => [1]
 => ? = 0 + 1
[-3,1,2] => [-3,2,-1] => [-2,-3,-1] => []
 => ? = 0 + 1
[-3,-1,2] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[-3,-1,-2] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[3,2,1] => [3,2,1] => [2,-3,1] => []
 => ? = 0 + 1
[3,-2,1] => [-2,-1,3] => [2,-1,3] => [1]
 => ? = 0 + 1
[3,-2,-1] => [-1,-2,3] => [-1,-2,3] => [1]
 => ? = 0 + 1
[-3,2,1] => [-3,2,-1] => [-2,-3,-1] => []
 => ? = 0 + 1
[-3,-2,1] => [-2,-1,-3] => [2,-1,-3] => []
 => ? = 1 + 1
[-3,-2,-1] => [-1,-2,-3] => [-1,-2,-3] => []
 => ? = 0 + 1
[1,2,-3,4] => [1,2,-3,-4] => [1,2,-3,-4] => [1,1]
 => ? = 0 + 1
[1,2,-3,-4] => [1,2,-3,-4] => [1,2,-3,-4] => [1,1]
 => ? = 0 + 1
[1,-2,3,4] => [1,-2,-3,4] => [1,-2,-3,4] => [1,1]
 => ? = 0 + 1
[1,-2,3,-4] => [1,-2,-3,-4] => [1,-2,-3,-4] => [1]
 => ? = 0 + 1
[1,-2,-3,4] => [1,-2,-3,-4] => [1,-2,-3,-4] => [1]
 => ? = 0 + 1
[1,2,3,-4,5] => [1,2,3,-4,-5] => [1,2,3,-4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,2,3,-4,-5] => [1,2,3,-4,-5] => [1,2,3,-4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,2,-3,4,5] => [1,2,-3,-4,5] => [1,2,-3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[1,-2,3,4,5] => [1,-2,-3,4,5] => [1,-2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,2,3,4,5] => [-1,-2,3,4,5] => [-1,-2,3,4,5] => [1,1,1]
 => 1 = 0 + 1
[1,2,3,-5,-4] => [1,2,3,-4,-5] => [1,2,3,-4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,2,-3,5,4] => [1,2,-3,-4,5] => [1,2,-3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[1,2,4,-3,5] => [1,2,-3,4,-5] => [1,2,-3,4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,2,4,-3,-5] => [1,2,-3,4,-5] => [1,2,-3,4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,-2,4,3,5] => [1,-2,-3,4,5] => [1,-2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,2,4,3,-5] => [-1,-2,4,3,-5] => [-1,-4,-2,3,-5] => [3]
 => 1 = 0 + 1
[1,2,4,-5,-3] => [1,2,-3,4,-5] => [1,2,-3,4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,2,5,-3,4] => [1,2,-3,-4,5] => [1,2,-3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[1,2,5,-3,-4] => [1,2,-3,-4,5] => [1,2,-3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,2,5,3,-4] => [-1,-2,5,-4,3] => [-1,-2,4,5,3] => [3]
 => 1 = 0 + 1
[1,2,5,-4,-3] => [1,2,-3,-4,5] => [1,2,-3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,2,5,4,-3] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[1,3,-2,4,5] => [1,-2,3,-4,5] => [1,-2,3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,3,2,4,5] => [-1,-2,3,4,5] => [-1,-2,3,4,5] => [1,1,1]
 => 1 = 0 + 1
[1,3,-2,5,4] => [1,-2,3,-4,5] => [1,-2,3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[1,3,4,2,5] => [1,4,3,2,5] => [3,-4,1,2,5] => [2,1]
 => 1 = 0 + 1
[1,3,4,-2,5] => [1,-2,3,4,-5] => [1,-2,3,4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,3,4,-2,-5] => [1,-2,3,4,-5] => [1,-2,3,4,-5] => [1,1,1]
 => 1 = 0 + 1
[-1,3,4,2,-5] => [-1,-2,4,3,-5] => [-1,-4,-2,3,-5] => [3]
 => 1 = 0 + 1
[1,3,4,-5,-2] => [1,-2,3,4,-5] => [1,-2,3,4,-5] => [1,1,1]
 => 1 = 0 + 1
[1,3,5,-2,4] => [1,-2,3,-4,5] => [1,-2,3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[1,3,5,-2,-4] => [1,-2,3,-4,5] => [1,-2,3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,3,5,2,-4] => [-1,-2,5,-4,3] => [-1,-2,4,5,3] => [3]
 => 1 = 0 + 1
[1,3,5,-4,-2] => [1,-2,3,-4,5] => [1,-2,3,-4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,3,5,4,-2] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[1,4,2,3,5] => [1,4,3,2,5] => [3,-4,1,2,5] => [2,1]
 => 1 = 0 + 1
[1,4,-2,3,5] => [1,-2,-3,4,5] => [1,-2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,4,2,3,-5] => [-1,-2,4,3,-5] => [-1,-4,-2,3,-5] => [3]
 => 1 = 0 + 1
[1,4,-2,5,3] => [1,-2,-3,4,5] => [1,-2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[1,4,3,2,5] => [1,4,3,2,5] => [3,-4,1,2,5] => [2,1]
 => 1 = 0 + 1
[-1,4,3,2,-5] => [-1,-2,4,3,-5] => [-1,-4,-2,3,-5] => [3]
 => 1 = 0 + 1
[1,4,5,-2,3] => [1,-2,-3,4,5] => [1,-2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[1,4,5,-2,-3] => [1,-2,-3,4,5] => [1,-2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,4,5,2,-3] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[1,4,5,-3,-2] => [1,-2,-3,4,5] => [1,-2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[-1,4,5,3,-2] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[-1,5,2,3,-4] => [-1,-2,5,-4,3] => [-1,-2,4,5,3] => [3]
 => 1 = 0 + 1
[-1,5,2,4,-3] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[-1,5,3,2,-4] => [-1,-2,5,-4,3] => [-1,-2,4,5,3] => [3]
 => 1 = 0 + 1
[-1,5,3,4,-2] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[-1,5,4,2,-3] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[-1,5,4,3,-2] => [-1,-2,-3,5,4] => [-1,-2,-5,-3,4] => [3]
 => 1 = 0 + 1
[2,1,3,4,5] => [2,1,3,4,5] => [-2,1,3,4,5] => [1,1,1]
 => 1 = 0 + 1
[2,-1,3,4,5] => [-1,2,-3,4,5] => [-1,2,-3,4,5] => [1,1,1]
 => 1 = 0 + 1
[-2,1,3,4,5] => [-2,-1,3,4,5] => [2,-1,3,4,5] => [1,1,1]
 => 1 = 0 + 1

Description

The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. Two colourings are considered equal, if they are obtained by an action of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.