Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000668
Mapping
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00167: Signed permutations —inverse Kreweras complement⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,-2] => [1,-2] => [-2,-1] => [2]
 => 2
[2,-1] => [-1,2] => [2,1] => [2]
 => 2
[1,2,-3] => [1,2,-3] => [2,-3,-1] => [3]
 => 3
[-1,2,-3] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[-1,-2,3] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[-1,-2,-3] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[1,3,-2] => [1,-2,3] => [-2,3,-1] => [3]
 => 3
[1,-3,2] => [1,-3,-2] => [-3,-2,-1] => [2]
 => 2
[-1,3,-2] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[-1,-3,2] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[-1,-3,-2] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[2,1,-3] => [2,1,-3] => [1,-3,-2] => [2,1]
 => 2
[-2,1,3] => [-2,-1,3] => [-1,3,2] => [2]
 => 2
[-2,-1,3] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[-2,-1,-3] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[2,3,1] => [3,2,1] => [2,1,-3] => [2]
 => 2
[2,3,-1] => [-1,2,3] => [2,3,1] => [3]
 => 3
[-2,3,1] => [-2,-1,3] => [-1,3,2] => [2]
 => 2
[-2,3,-1] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[-2,-3,-1] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[3,1,2] => [3,2,1] => [2,1,-3] => [2]
 => 2
[-3,1,-2] => [-3,-2,-1] => [-2,-1,3] => [2,1]
 => 2
[-3,-1,2] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[-3,-1,-2] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[3,2,1] => [3,2,1] => [2,1,-3] => [2]
 => 2
[3,2,-1] => [-1,3,2] => [3,2,1] => [2,1]
 => 2
[3,-2,1] => [-2,-1,3] => [-1,3,2] => [2]
 => 2
[-3,-2,-1] => [-1,-2,-3] => [-2,-3,1] => [3]
 => 3
[1,2,3,-4] => [1,2,3,-4] => [2,3,-4,-1] => [4]
 => 4
[1,-2,3,-4] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[1,-2,-3,4] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[1,-2,-3,-4] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[-1,2,3,-4] => [-1,-2,3,-4] => [-2,3,-4,1] => [4]
 => 4
[1,2,4,-3] => [1,2,-3,4] => [2,-3,4,-1] => [4]
 => 4
[1,2,-4,3] => [1,2,-4,-3] => [2,-4,-3,-1] => [3]
 => 3
[1,-2,4,-3] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[1,-2,-4,3] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[1,-2,-4,-3] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[-1,2,4,-3] => [-1,-2,-3,4] => [-2,-3,4,1] => [4]
 => 4
[-1,2,-4,3] => [-1,-2,-4,-3] => [-2,-4,-3,1] => [3]
 => 3
[1,3,2,-4] => [1,3,2,-4] => [3,2,-4,-1] => [3,1]
 => 3
[1,-3,2,4] => [1,-3,-2,4] => [-3,-2,4,-1] => [3]
 => 3
[1,-3,-2,4] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[1,-3,-2,-4] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
[-1,3,2,-4] => [-1,-2,3,-4] => [-2,3,-4,1] => [4]
 => 4
[1,3,4,2] => [1,4,3,2] => [4,3,2,-1] => [2]
 => 2
[1,3,4,-2] => [1,-2,3,4] => [-2,3,4,-1] => [4]
 => 4
[1,3,-4,2] => [1,-4,3,-2] => [-4,3,-2,-1] => [2]
 => 2
[1,-3,4,2] => [1,-3,-2,4] => [-3,-2,4,-1] => [3]
 => 3
[1,-3,4,-2] => [1,-2,-3,-4] => [-2,-3,-4,-1] => [4]
 => 4
Description
The least common multiple of the parts of the partition.
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: 17% ●values known / values provided: 28%●distinct values known / distinct values provided: 17%
Values
[1,-2] => [1,-2] => [1]
 => []
 => ? = 2 + 1
[2,-1] => [-1,2] => [1]
 => []
 => ? = 2 + 1
[1,2,-3] => [1,2,-3] => [1]
 => []
 => ? = 3 + 1
[-1,2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[-1,-2,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[1,3,-2] => [1,-2,3] => [1]
 => []
 => ? = 3 + 1
[1,-3,2] => [1,-3,-2] => []
 => ?
 => ? = 2 + 1
[-1,3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[-1,-3,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[-1,-3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[2,1,-3] => [2,1,-3] => [1]
 => []
 => ? = 2 + 1
[-2,1,3] => [-2,-1,3] => []
 => ?
 => ? = 2 + 1
[-2,-1,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[-2,-1,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[2,3,1] => [3,2,1] => []
 => ?
 => ? = 2 + 1
[2,3,-1] => [-1,2,3] => [1]
 => []
 => ? = 3 + 1
[-2,3,1] => [-2,-1,3] => []
 => ?
 => ? = 2 + 1
[-2,3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[-2,-3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[3,1,2] => [3,2,1] => []
 => ?
 => ? = 2 + 1
[-3,1,-2] => [-3,-2,-1] => [1]
 => []
 => ? = 2 + 1
[-3,-1,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[-3,-1,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[3,2,1] => [3,2,1] => []
 => ?
 => ? = 2 + 1
[3,2,-1] => [-1,3,2] => [1]
 => []
 => ? = 2 + 1
[3,-2,1] => [-2,-1,3] => []
 => ?
 => ? = 2 + 1
[-3,-2,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 + 1
[1,2,3,-4] => [1,2,3,-4] => [1]
 => []
 => ? = 4 + 1
[1,-2,3,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[1,-2,-3,4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[-1,2,3,-4] => [-1,-2,3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[1,2,4,-3] => [1,2,-3,4] => [1]
 => []
 => ? = 4 + 1
[1,2,-4,3] => [1,2,-4,-3] => []
 => ?
 => ? = 3 + 1
[1,-2,4,-3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[1,-2,-4,3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[1,-2,-4,-3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[-1,2,4,-3] => [-1,-2,-3,4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[-1,2,-4,3] => [-1,-2,-4,-3] => [1,1]
 => [1]
 => ? = 3 + 1
[1,3,2,-4] => [1,3,2,-4] => [1]
 => []
 => ? = 3 + 1
[1,-3,2,4] => [1,-3,-2,4] => []
 => ?
 => ? = 3 + 1
[1,-3,-2,4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[1,-3,-2,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[-1,3,2,-4] => [-1,-2,3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[1,3,4,2] => [1,4,3,2] => []
 => ?
 => ? = 2 + 1
[1,3,4,-2] => [1,-2,3,4] => [1]
 => []
 => ? = 4 + 1
[1,3,-4,2] => [1,-4,3,-2] => []
 => ?
 => ? = 2 + 1
[1,-3,4,2] => [1,-3,-2,4] => []
 => ?
 => ? = 3 + 1
[1,-3,4,-2] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 + 1
[-1,2,-3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,4,3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,4,-5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,-5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,5,3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-5,3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-5,3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,-5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,2,-5,-4,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,5,4,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 1
[-1,-2,5,-4,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 6 = 5 + 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.
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: 17% ●values known / values provided: 28%●distinct values known / distinct values provided: 17%
Values
[1,-2] => [1,-2] => [1]
 => []
 => ? = 2 - 2
[2,-1] => [-1,2] => [1]
 => []
 => ? = 2 - 2
[1,2,-3] => [1,2,-3] => [1]
 => []
 => ? = 3 - 2
[-1,2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[-1,-2,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[1,3,-2] => [1,-2,3] => [1]
 => []
 => ? = 3 - 2
[1,-3,2] => [1,-3,-2] => []
 => ?
 => ? = 2 - 2
[-1,3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[-1,-3,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[-1,-3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[2,1,-3] => [2,1,-3] => [1]
 => []
 => ? = 2 - 2
[-2,1,3] => [-2,-1,3] => []
 => ?
 => ? = 2 - 2
[-2,-1,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[-2,-1,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[2,3,1] => [3,2,1] => []
 => ?
 => ? = 2 - 2
[2,3,-1] => [-1,2,3] => [1]
 => []
 => ? = 3 - 2
[-2,3,1] => [-2,-1,3] => []
 => ?
 => ? = 2 - 2
[-2,3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[-2,-3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[3,1,2] => [3,2,1] => []
 => ?
 => ? = 2 - 2
[-3,1,-2] => [-3,-2,-1] => [1]
 => []
 => ? = 2 - 2
[-3,-1,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[-3,-1,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[3,2,1] => [3,2,1] => []
 => ?
 => ? = 2 - 2
[3,2,-1] => [-1,3,2] => [1]
 => []
 => ? = 2 - 2
[3,-2,1] => [-2,-1,3] => []
 => ?
 => ? = 2 - 2
[-3,-2,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 2
[1,2,3,-4] => [1,2,3,-4] => [1]
 => []
 => ? = 4 - 2
[1,-2,3,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[1,-2,-3,4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[-1,2,3,-4] => [-1,-2,3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[1,2,4,-3] => [1,2,-3,4] => [1]
 => []
 => ? = 4 - 2
[1,2,-4,3] => [1,2,-4,-3] => []
 => ?
 => ? = 3 - 2
[1,-2,4,-3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[1,-2,-4,3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[1,-2,-4,-3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[-1,2,4,-3] => [-1,-2,-3,4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[-1,2,-4,3] => [-1,-2,-4,-3] => [1,1]
 => [1]
 => ? = 3 - 2
[1,3,2,-4] => [1,3,2,-4] => [1]
 => []
 => ? = 3 - 2
[1,-3,2,4] => [1,-3,-2,4] => []
 => ?
 => ? = 3 - 2
[1,-3,-2,4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[1,-3,-2,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[-1,3,2,-4] => [-1,-2,3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[1,3,4,2] => [1,4,3,2] => []
 => ?
 => ? = 2 - 2
[1,3,4,-2] => [1,-2,3,4] => [1]
 => []
 => ? = 4 - 2
[1,3,-4,2] => [1,-4,3,-2] => []
 => ?
 => ? = 2 - 2
[1,-3,4,2] => [1,-3,-2,4] => []
 => ?
 => ? = 3 - 2
[1,-3,4,-2] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 2
[-1,2,-3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,4,3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,4,-5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,-5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,5,3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-5,3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-5,3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,-5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,2,-5,-4,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,5,4,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
[-1,-2,5,-4,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3 = 5 - 2
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: 17% ●values known / values provided: 28%●distinct values known / distinct values provided: 17%
Values
[1,-2] => [1,-2] => [1]
 => []
 => ? = 2 - 5
[2,-1] => [-1,2] => [1]
 => []
 => ? = 2 - 5
[1,2,-3] => [1,2,-3] => [1]
 => []
 => ? = 3 - 5
[-1,2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[-1,-2,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[-1,-2,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[1,3,-2] => [1,-2,3] => [1]
 => []
 => ? = 3 - 5
[1,-3,2] => [1,-3,-2] => []
 => ?
 => ? = 2 - 5
[-1,3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[-1,-3,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[-1,-3,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[2,1,-3] => [2,1,-3] => [1]
 => []
 => ? = 2 - 5
[-2,1,3] => [-2,-1,3] => []
 => ?
 => ? = 2 - 5
[-2,-1,3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[-2,-1,-3] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[2,3,1] => [3,2,1] => []
 => ?
 => ? = 2 - 5
[2,3,-1] => [-1,2,3] => [1]
 => []
 => ? = 3 - 5
[-2,3,1] => [-2,-1,3] => []
 => ?
 => ? = 2 - 5
[-2,3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[-2,-3,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[3,1,2] => [3,2,1] => []
 => ?
 => ? = 2 - 5
[-3,1,-2] => [-3,-2,-1] => [1]
 => []
 => ? = 2 - 5
[-3,-1,2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[-3,-1,-2] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[3,2,1] => [3,2,1] => []
 => ?
 => ? = 2 - 5
[3,2,-1] => [-1,3,2] => [1]
 => []
 => ? = 2 - 5
[3,-2,1] => [-2,-1,3] => []
 => ?
 => ? = 2 - 5
[-3,-2,-1] => [-1,-2,-3] => [1,1,1]
 => [1,1]
 => ? = 3 - 5
[1,2,3,-4] => [1,2,3,-4] => [1]
 => []
 => ? = 4 - 5
[1,-2,3,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[1,-2,-3,4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[-1,2,3,-4] => [-1,-2,3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[1,2,4,-3] => [1,2,-3,4] => [1]
 => []
 => ? = 4 - 5
[1,2,-4,3] => [1,2,-4,-3] => []
 => ?
 => ? = 3 - 5
[1,-2,4,-3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[1,-2,-4,3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[1,-2,-4,-3] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[-1,2,4,-3] => [-1,-2,-3,4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[-1,2,-4,3] => [-1,-2,-4,-3] => [1,1]
 => [1]
 => ? = 3 - 5
[1,3,2,-4] => [1,3,2,-4] => [1]
 => []
 => ? = 3 - 5
[1,-3,2,4] => [1,-3,-2,4] => []
 => ?
 => ? = 3 - 5
[1,-3,-2,4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[1,-3,-2,-4] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[-1,3,2,-4] => [-1,-2,3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[1,3,4,2] => [1,4,3,2] => []
 => ?
 => ? = 2 - 5
[1,3,4,-2] => [1,-2,3,4] => [1]
 => []
 => ? = 4 - 5
[1,3,-4,2] => [1,-4,3,-2] => []
 => ?
 => ? = 2 - 5
[1,-3,4,2] => [1,-3,-2,4] => []
 => ?
 => ? = 3 - 5
[1,-3,4,-2] => [1,-2,-3,-4] => [1,1,1]
 => [1,1]
 => ? = 4 - 5
[-1,2,-3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,-4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,-4,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,-5,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-3,-5,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,4,3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,-3,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,-3,-5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,4,-5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,-5,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-4,-5,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,5,3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-5,3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-5,3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-5,-3,4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,-5,-3,-4] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,2,-5,-4,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,5,4,-3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
[-1,-2,5,-4,3] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0 = 5 - 5
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.