Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St000073
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000073: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-1] => [1]
 => [[1]]
 => [[1]]
 => 0
[1,-2] => [1]
 => [[1]]
 => [[1]]
 => 0
[-1,2] => [1]
 => [[1]]
 => [[1]]
 => 0
[-1,-2] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[2,-1] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[-2,1] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[1,2,-3] => [1]
 => [[1]]
 => [[1]]
 => 0
[1,-2,3] => [1]
 => [[1]]
 => [[1]]
 => 0
[1,-2,-3] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[-1,2,3] => [1]
 => [[1]]
 => [[1]]
 => 0
[-1,2,-3] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[-1,-2,3] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[-1,-2,-3] => [1,1,1]
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 3
[1,3,-2] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[1,-3,2] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[-1,3,2] => [1]
 => [[1]]
 => [[1]]
 => 0
[-1,3,-2] => [2,1]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[-1,-3,2] => [2,1]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[-1,-3,-2] => [1]
 => [[1]]
 => [[1]]
 => 0
[2,1,-3] => [1]
 => [[1]]
 => [[1]]
 => 0
[2,-1,3] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[2,-1,-3] => [2,1]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[-2,1,3] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[-2,1,-3] => [2,1]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[-2,-1,-3] => [1]
 => [[1]]
 => [[1]]
 => 0
[2,3,-1] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[2,-3,1] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[-2,3,1] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[-2,-3,-1] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[3,1,-2] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[3,-1,2] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[-3,1,2] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[-3,-1,-2] => [3]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[3,2,-1] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[3,-2,1] => [1]
 => [[1]]
 => [[1]]
 => 0
[3,-2,-1] => [2,1]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[-3,2,1] => [2]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[-3,-2,1] => [2,1]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[-3,-2,-1] => [1]
 => [[1]]
 => [[1]]
 => 0
[1,2,3,-4] => [1]
 => [[1]]
 => [[1]]
 => 0
[1,2,-3,4] => [1]
 => [[1]]
 => [[1]]
 => 0
[1,2,-3,-4] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[1,-2,3,4] => [1]
 => [[1]]
 => [[1]]
 => 0
[1,-2,3,-4] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[1,-2,-3,4] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[1,-2,-3,-4] => [1,1,1]
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 3
[-1,2,3,4] => [1]
 => [[1]]
 => [[1]]
 => 0
[-1,2,3,-4] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[-1,2,-3,4] => [1,1]
 => [[1],[2]]
 => [[1,1],[1]]
 => 1
[-1,2,-3,-4] => [1,1,1]
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 3
Description
The number of boxed entries. An entry of a Gelfand-Tsetlin pattern is boxed if $a_{i,j} = a_{i-1,j-1}$ (the northwest neighbor is the same).
Matching statistic: St001491
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 14% ●values known / values provided: 30%●distinct values known / distinct values provided: 14%
Values
[-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-2] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[2,-1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[-2,1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[1,2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,-3] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 3
[1,3,-2] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[1,-3,2] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[-1,3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,-2] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-1,-3,2] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-1,-3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,1,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,-1,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[2,-1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-2,1,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[-2,1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-2,-1,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[2,-3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-2,3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-2,-3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[3,1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[3,-1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-3,1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-3,-1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[3,2,-1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[3,-2,1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[3,-2,-1] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-3,2,1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[-3,-2,1] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-3,-2,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,2,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,2,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,2,-3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,-2,3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,-2,-3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 3
[-1,2,3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,2,-3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 3
[-1,-2,3,4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 3
[-1,-2,-3,4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 3
[-1,-2,-3,-4] => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1011110000 => ? = 6
[1,2,4,-3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[1,2,-4,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[1,-2,4,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,4,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[1,-2,-4,3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[1,-2,-4,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,4,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,4,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-1,2,-4,3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[-1,2,-4,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-2,4,3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,4,-3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 5
[-1,-2,-4,3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 5
[-1,-2,-4,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,3,2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,3,-2,4] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 0
[1,3,-2,-4] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2
[1,-3,-2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,2,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-3,-2,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,4,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,-4,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-3,4,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-3,-4,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,4,2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,4,-2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-4,2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-4,-2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,4,-3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-4,-3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,4,3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-4,3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,1,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,1,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-1,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-1,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,3,1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,-3,-1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,3,-1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-3,1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,4,-3,1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,-4,-3,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,4,-3,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-4,-3,1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[3,1,2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[3,-1,-2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Matching statistic: St001605
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 14%
Values
[-1] => [1]
 => [1]
 => []
 => ? = 0 - 1
[1,-2] => [1]
 => [1]
 => []
 => ? = 0 - 1
[-1,2] => [1]
 => [1]
 => []
 => ? = 0 - 1
[-1,-2] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[2,-1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[-2,1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[1,2,-3] => [1]
 => [1]
 => []
 => ? = 0 - 1
[1,-2,3] => [1]
 => [1]
 => []
 => ? = 0 - 1
[1,-2,-3] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[-1,2,3] => [1]
 => [1]
 => []
 => ? = 0 - 1
[-1,2,-3] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[-1,-2,3] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[-1,-2,-3] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 1
[1,3,-2] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[1,-3,2] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[-1,3,2] => [1]
 => [1]
 => []
 => ? = 0 - 1
[-1,3,-2] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 1
[-1,-3,2] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 1
[-1,-3,-2] => [1]
 => [1]
 => []
 => ? = 0 - 1
[2,1,-3] => [1]
 => [1]
 => []
 => ? = 0 - 1
[2,-1,3] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[2,-1,-3] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 1
[-2,1,3] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[-2,1,-3] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 1
[-2,-1,-3] => [1]
 => [1]
 => []
 => ? = 0 - 1
[2,3,-1] => [3]
 => [3]
 => []
 => ? = 1 - 1
[2,-3,1] => [3]
 => [3]
 => []
 => ? = 1 - 1
[-2,3,1] => [3]
 => [3]
 => []
 => ? = 1 - 1
[-2,-3,-1] => [3]
 => [3]
 => []
 => ? = 1 - 1
[3,1,-2] => [3]
 => [3]
 => []
 => ? = 1 - 1
[3,-1,2] => [3]
 => [3]
 => []
 => ? = 1 - 1
[-3,1,2] => [3]
 => [3]
 => []
 => ? = 1 - 1
[-3,-1,-2] => [3]
 => [3]
 => []
 => ? = 1 - 1
[3,2,-1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[3,-2,1] => [1]
 => [1]
 => []
 => ? = 0 - 1
[3,-2,-1] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 1
[-3,2,1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 1
[-3,-2,1] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 1
[-3,-2,-1] => [1]
 => [1]
 => []
 => ? = 0 - 1
[1,2,3,-4] => [1]
 => [1]
 => []
 => ? = 0 - 1
[1,2,-3,4] => [1]
 => [1]
 => []
 => ? = 0 - 1
[1,2,-3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[1,-2,3,4] => [1]
 => [1]
 => []
 => ? = 0 - 1
[1,-2,3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[1,-2,-3,4] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[1,-2,-3,-4] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 1
[-1,2,3,4] => [1]
 => [1]
 => []
 => ? = 0 - 1
[-1,2,3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[-1,2,-3,4] => [1,1]
 => [2]
 => []
 => ? = 1 - 1
[-1,2,-3,-4] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 1
[2,-1,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[2,-1,-4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,-4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,4,-1,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,-4,-1,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,4,1,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,-4,1,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[4,3,-2,-1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[4,-3,2,-1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-4,3,-2,1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-4,-3,2,1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,3,-2,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,3,-2,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,-3,2,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,-3,2,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,4,5,-2,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,4,-5,-2,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,-4,5,2,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,-4,-5,2,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,5,4,-3,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,5,-4,3,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,-5,4,-3,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[1,-5,-4,3,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[2,-1,3,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[2,-1,3,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,3,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,3,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[2,-1,4,-3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[2,-1,-4,3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,4,-3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,-4,3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[2,-1,5,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[2,-1,-5,4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,5,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-2,1,-5,4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,2,-1,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,2,-1,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,2,1,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,2,1,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,4,-1,-2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,-4,-1,2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,4,1,-2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,-4,1,2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,5,-1,4,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[3,-5,-1,4,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,5,1,4,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[-3,-5,1,4,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[4,2,5,-1,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 1
[4,2,-5,-1,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 2 = 3 - 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
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 14%
Values
[-1] => [1]
 => [1]
 => []
 => ? = 0 - 2
[1,-2] => [1]
 => [1]
 => []
 => ? = 0 - 2
[-1,2] => [1]
 => [1]
 => []
 => ? = 0 - 2
[-1,-2] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[2,-1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[-2,1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[1,2,-3] => [1]
 => [1]
 => []
 => ? = 0 - 2
[1,-2,3] => [1]
 => [1]
 => []
 => ? = 0 - 2
[1,-2,-3] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[-1,2,3] => [1]
 => [1]
 => []
 => ? = 0 - 2
[-1,2,-3] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[-1,-2,3] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[-1,-2,-3] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 2
[1,3,-2] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[1,-3,2] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[-1,3,2] => [1]
 => [1]
 => []
 => ? = 0 - 2
[-1,3,-2] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 2
[-1,-3,2] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 2
[-1,-3,-2] => [1]
 => [1]
 => []
 => ? = 0 - 2
[2,1,-3] => [1]
 => [1]
 => []
 => ? = 0 - 2
[2,-1,3] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[2,-1,-3] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 2
[-2,1,3] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[-2,1,-3] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 2
[-2,-1,-3] => [1]
 => [1]
 => []
 => ? = 0 - 2
[2,3,-1] => [3]
 => [3]
 => []
 => ? = 1 - 2
[2,-3,1] => [3]
 => [3]
 => []
 => ? = 1 - 2
[-2,3,1] => [3]
 => [3]
 => []
 => ? = 1 - 2
[-2,-3,-1] => [3]
 => [3]
 => []
 => ? = 1 - 2
[3,1,-2] => [3]
 => [3]
 => []
 => ? = 1 - 2
[3,-1,2] => [3]
 => [3]
 => []
 => ? = 1 - 2
[-3,1,2] => [3]
 => [3]
 => []
 => ? = 1 - 2
[-3,-1,-2] => [3]
 => [3]
 => []
 => ? = 1 - 2
[3,2,-1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[3,-2,1] => [1]
 => [1]
 => []
 => ? = 0 - 2
[3,-2,-1] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 2
[-3,2,1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 2
[-3,-2,1] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 2
[-3,-2,-1] => [1]
 => [1]
 => []
 => ? = 0 - 2
[1,2,3,-4] => [1]
 => [1]
 => []
 => ? = 0 - 2
[1,2,-3,4] => [1]
 => [1]
 => []
 => ? = 0 - 2
[1,2,-3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[1,-2,3,4] => [1]
 => [1]
 => []
 => ? = 0 - 2
[1,-2,3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[1,-2,-3,4] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[1,-2,-3,-4] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 2
[-1,2,3,4] => [1]
 => [1]
 => []
 => ? = 0 - 2
[-1,2,3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[-1,2,-3,4] => [1,1]
 => [2]
 => []
 => ? = 1 - 2
[-1,2,-3,-4] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 2
[2,-1,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[2,-1,-4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,-4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,4,-1,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,-4,-1,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,4,1,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,-4,1,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[4,3,-2,-1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[4,-3,2,-1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-4,3,-2,1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-4,-3,2,1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,3,-2,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,3,-2,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,-3,2,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,-3,2,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,4,5,-2,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,4,-5,-2,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,-4,5,2,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,-4,-5,2,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,5,4,-3,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,5,-4,3,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,-5,4,-3,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[1,-5,-4,3,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[2,-1,3,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[2,-1,3,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,3,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,3,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[2,-1,4,-3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[2,-1,-4,3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,4,-3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,-4,3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[2,-1,5,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[2,-1,-5,4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,5,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-2,1,-5,4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,2,-1,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,2,-1,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,2,1,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,2,1,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,4,-1,-2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,-4,-1,2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,4,1,-2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,-4,1,2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,5,-1,4,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[3,-5,-1,4,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,5,1,4,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[-3,-5,1,4,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[4,2,5,-1,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 2
[4,2,-5,-1,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 3 - 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
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 14%
Values
[-1] => [1]
 => [1]
 => []
 => ? = 0 - 3
[1,-2] => [1]
 => [1]
 => []
 => ? = 0 - 3
[-1,2] => [1]
 => [1]
 => []
 => ? = 0 - 3
[-1,-2] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[2,-1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[-2,1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[1,2,-3] => [1]
 => [1]
 => []
 => ? = 0 - 3
[1,-2,3] => [1]
 => [1]
 => []
 => ? = 0 - 3
[1,-2,-3] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[-1,2,3] => [1]
 => [1]
 => []
 => ? = 0 - 3
[-1,2,-3] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[-1,-2,3] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[-1,-2,-3] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 3
[1,3,-2] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[1,-3,2] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[-1,3,2] => [1]
 => [1]
 => []
 => ? = 0 - 3
[-1,3,-2] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 3
[-1,-3,2] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 3
[-1,-3,-2] => [1]
 => [1]
 => []
 => ? = 0 - 3
[2,1,-3] => [1]
 => [1]
 => []
 => ? = 0 - 3
[2,-1,3] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[2,-1,-3] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 3
[-2,1,3] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[-2,1,-3] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 3
[-2,-1,-3] => [1]
 => [1]
 => []
 => ? = 0 - 3
[2,3,-1] => [3]
 => [3]
 => []
 => ? = 1 - 3
[2,-3,1] => [3]
 => [3]
 => []
 => ? = 1 - 3
[-2,3,1] => [3]
 => [3]
 => []
 => ? = 1 - 3
[-2,-3,-1] => [3]
 => [3]
 => []
 => ? = 1 - 3
[3,1,-2] => [3]
 => [3]
 => []
 => ? = 1 - 3
[3,-1,2] => [3]
 => [3]
 => []
 => ? = 1 - 3
[-3,1,2] => [3]
 => [3]
 => []
 => ? = 1 - 3
[-3,-1,-2] => [3]
 => [3]
 => []
 => ? = 1 - 3
[3,2,-1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[3,-2,1] => [1]
 => [1]
 => []
 => ? = 0 - 3
[3,-2,-1] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 3
[-3,2,1] => [2]
 => [1,1]
 => [1]
 => ? = 0 - 3
[-3,-2,1] => [2,1]
 => [1,1,1]
 => [1,1]
 => ? = 2 - 3
[-3,-2,-1] => [1]
 => [1]
 => []
 => ? = 0 - 3
[1,2,3,-4] => [1]
 => [1]
 => []
 => ? = 0 - 3
[1,2,-3,4] => [1]
 => [1]
 => []
 => ? = 0 - 3
[1,2,-3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[1,-2,3,4] => [1]
 => [1]
 => []
 => ? = 0 - 3
[1,-2,3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[1,-2,-3,4] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[1,-2,-3,-4] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 3
[-1,2,3,4] => [1]
 => [1]
 => []
 => ? = 0 - 3
[-1,2,3,-4] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[-1,2,-3,4] => [1,1]
 => [2]
 => []
 => ? = 1 - 3
[-1,2,-3,-4] => [1,1,1]
 => [2,1]
 => [1]
 => ? = 3 - 3
[2,-1,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[2,-1,-4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,-4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,4,-1,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,-4,-1,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,4,1,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,-4,1,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[4,3,-2,-1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[4,-3,2,-1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-4,3,-2,1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-4,-3,2,1] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,3,-2,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,3,-2,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,-3,2,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,-3,2,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,4,5,-2,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,4,-5,-2,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,-4,5,2,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,-4,-5,2,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,5,4,-3,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,5,-4,3,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,-5,4,-3,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[1,-5,-4,3,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[2,-1,3,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[2,-1,3,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,3,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,3,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[2,-1,4,-3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[2,-1,-4,3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,4,-3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,-4,3,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[2,-1,5,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[2,-1,-5,4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,5,4,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-2,1,-5,4,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,2,-1,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,2,-1,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,2,1,5,-4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,2,1,-5,4] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,4,-1,-2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,-4,-1,2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,4,1,-2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,-4,1,2,5] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,5,-1,4,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[3,-5,-1,4,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,5,1,4,-2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[-3,-5,1,4,2] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[4,2,5,-1,-3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
[4,2,-5,-1,3] => [2,2]
 => [1,1,1,1]
 => [1,1,1]
 => 0 = 3 - 3
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.