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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St001940

Mapping

Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St001940: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

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

Description

The number of distinct parts that are equal to their multiplicity in the integer partition.

Matching statistic: St000815

Mapping

Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000815: Integer partitions ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 100%

Values

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

Description

The number of semistandard Young tableaux of partition weight of given shape. The weight of a semistandard Young tableaux is the sequence

$(m_1, m_2,\dots)$ , where

$m_i$ is the number of occurrences of the number

$i$ in the tableau. This statistic counts those tableaux whose weight is a weakly decreasing sequence. Alternatively, this is the sum of the entries in the column specified by the partition of the change of basis matrix from Schur functions to monomial symmetric functions.

Matching statistic: St001603

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
St001603: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 33%

Values

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

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: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 33%

Values

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

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: St001605

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
St001605: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 33%

Values

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

Description

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