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Your data matches 21 different statistics following compositions of up to 3 maps.
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Matching statistic: St000707
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(load all 5 compositions to match this statistic)
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000707: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000707: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,2,3,-4] => [1,1,1]
=> [1,1]
=> 1
[1,2,-3,4] => [1,1,1]
=> [1,1]
=> 1
[1,-2,3,4] => [1,1,1]
=> [1,1]
=> 1
[-1,2,3,4] => [1,1,1]
=> [1,1]
=> 1
[1,2,4,3] => [2,1,1]
=> [1,1]
=> 1
[1,2,-4,-3] => [2,1,1]
=> [1,1]
=> 1
[1,3,2,4] => [2,1,1]
=> [1,1]
=> 1
[1,-3,-2,4] => [2,1,1]
=> [1,1]
=> 1
[1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,-4,3,-2] => [2,1,1]
=> [1,1]
=> 1
[2,1,3,4] => [2,1,1]
=> [1,1]
=> 1
[-2,-1,3,4] => [2,1,1]
=> [1,1]
=> 1
[2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,-4,-3] => [2,2]
=> [2]
=> 2
[-2,-1,4,3] => [2,2]
=> [2]
=> 2
[-2,-1,-4,-3] => [2,2]
=> [2]
=> 2
[3,2,1,4] => [2,1,1]
=> [1,1]
=> 1
[-3,2,-1,4] => [2,1,1]
=> [1,1]
=> 1
[3,4,1,2] => [2,2]
=> [2]
=> 2
[3,-4,1,-2] => [2,2]
=> [2]
=> 2
[-3,4,-1,2] => [2,2]
=> [2]
=> 2
[-3,-4,-1,-2] => [2,2]
=> [2]
=> 2
[4,2,3,1] => [2,1,1]
=> [1,1]
=> 1
[-4,2,3,-1] => [2,1,1]
=> [1,1]
=> 1
[4,3,2,1] => [2,2]
=> [2]
=> 2
[4,-3,-2,1] => [2,2]
=> [2]
=> 2
[-4,3,2,-1] => [2,2]
=> [2]
=> 2
[-4,-3,-2,-1] => [2,2]
=> [2]
=> 2
[1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,2,3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,2,3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,2,3,-4,-5] => [1,1,1]
=> [1,1]
=> 1
[1,2,-3,4,5] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,2,-3,4,-5] => [1,1,1]
=> [1,1]
=> 1
[1,2,-3,-4,5] => [1,1,1]
=> [1,1]
=> 1
[1,-2,3,4,5] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,-2,3,4,-5] => [1,1,1]
=> [1,1]
=> 1
[1,-2,3,-4,5] => [1,1,1]
=> [1,1]
=> 1
[1,-2,-3,4,5] => [1,1,1]
=> [1,1]
=> 1
[-1,2,3,4,5] => [1,1,1,1]
=> [1,1,1]
=> 1
[-1,2,3,4,-5] => [1,1,1]
=> [1,1]
=> 1
[-1,2,3,-4,5] => [1,1,1]
=> [1,1]
=> 1
[-1,2,-3,4,5] => [1,1,1]
=> [1,1]
=> 1
[-1,-2,3,4,5] => [1,1,1]
=> [1,1]
=> 1
[1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,2,3,5,-4] => [1,1,1]
=> [1,1]
=> 1
[1,2,3,-5,4] => [1,1,1]
=> [1,1]
=> 1
[1,2,3,-5,-4] => [2,1,1,1]
=> [1,1,1]
=> 1
Description
The product of the factorials of the parts.
Matching statistic: St001593
Mp00244: Signed permutations —bar⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
St001593: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 43%●distinct values known / distinct values provided: 29%
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
St001593: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 43%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [-1,-2,-3] => [1,1,1]
=> 0 = 1 - 1
[1,2,3,4] => [-1,-2,-3,-4] => [1,1,1,1]
=> 0 = 1 - 1
[1,2,3,-4] => [-1,-2,-3,4] => [1,1,1]
=> 0 = 1 - 1
[1,2,-3,4] => [-1,-2,3,-4] => [1,1,1]
=> 0 = 1 - 1
[1,-2,3,4] => [-1,2,-3,-4] => [1,1,1]
=> 0 = 1 - 1
[-1,2,3,4] => [1,-2,-3,-4] => [1,1,1]
=> 0 = 1 - 1
[1,2,4,3] => [-1,-2,-4,-3] => [1,1]
=> 0 = 1 - 1
[1,2,-4,-3] => [-1,-2,4,3] => [1,1]
=> 0 = 1 - 1
[1,3,2,4] => [-1,-3,-2,-4] => [1,1]
=> 0 = 1 - 1
[1,-3,-2,4] => [-1,3,2,-4] => [1,1]
=> 0 = 1 - 1
[1,4,3,2] => [-1,-4,-3,-2] => [1,1]
=> 0 = 1 - 1
[1,-4,3,-2] => [-1,4,-3,2] => [1,1]
=> 0 = 1 - 1
[2,1,3,4] => [-2,-1,-3,-4] => [1,1]
=> 0 = 1 - 1
[-2,-1,3,4] => [2,1,-3,-4] => [1,1]
=> 0 = 1 - 1
[2,1,4,3] => [-2,-1,-4,-3] => []
=> ? = 2 - 1
[2,1,-4,-3] => [-2,-1,4,3] => []
=> ? = 2 - 1
[-2,-1,4,3] => [2,1,-4,-3] => []
=> ? = 2 - 1
[-2,-1,-4,-3] => [2,1,4,3] => []
=> ? = 2 - 1
[3,2,1,4] => [-3,-2,-1,-4] => [1,1]
=> 0 = 1 - 1
[-3,2,-1,4] => [3,-2,1,-4] => [1,1]
=> 0 = 1 - 1
[3,4,1,2] => [-3,-4,-1,-2] => []
=> ? = 2 - 1
[3,-4,1,-2] => [-3,4,-1,2] => []
=> ? = 2 - 1
[-3,4,-1,2] => [3,-4,1,-2] => []
=> ? = 2 - 1
[-3,-4,-1,-2] => [3,4,1,2] => []
=> ? = 2 - 1
[4,2,3,1] => [-4,-2,-3,-1] => [1,1]
=> 0 = 1 - 1
[-4,2,3,-1] => [4,-2,-3,1] => [1,1]
=> 0 = 1 - 1
[4,3,2,1] => [-4,-3,-2,-1] => []
=> ? = 2 - 1
[4,-3,-2,1] => [-4,3,2,-1] => []
=> ? = 2 - 1
[-4,3,2,-1] => [4,-3,-2,1] => []
=> ? = 2 - 1
[-4,-3,-2,-1] => [4,3,2,1] => []
=> ? = 2 - 1
[1,2,3,4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> 0 = 1 - 1
[1,2,3,4,-5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> 0 = 1 - 1
[1,2,3,-4,5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> 0 = 1 - 1
[1,2,3,-4,-5] => [-1,-2,-3,4,5] => [1,1,1]
=> 0 = 1 - 1
[1,2,-3,4,5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> 0 = 1 - 1
[1,2,-3,4,-5] => [-1,-2,3,-4,5] => [1,1,1]
=> 0 = 1 - 1
[1,2,-3,-4,5] => [-1,-2,3,4,-5] => [1,1,1]
=> 0 = 1 - 1
[1,-2,3,4,5] => [-1,2,-3,-4,-5] => [1,1,1,1]
=> 0 = 1 - 1
[1,-2,3,4,-5] => [-1,2,-3,-4,5] => [1,1,1]
=> 0 = 1 - 1
[1,-2,3,-4,5] => [-1,2,-3,4,-5] => [1,1,1]
=> 0 = 1 - 1
[1,-2,-3,4,5] => [-1,2,3,-4,-5] => [1,1,1]
=> 0 = 1 - 1
[-1,2,3,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> 0 = 1 - 1
[-1,2,3,4,-5] => [1,-2,-3,-4,5] => [1,1,1]
=> 0 = 1 - 1
[-1,2,3,-4,5] => [1,-2,-3,4,-5] => [1,1,1]
=> 0 = 1 - 1
[-1,2,-3,4,5] => [1,-2,3,-4,-5] => [1,1,1]
=> 0 = 1 - 1
[-1,-2,3,4,5] => [1,2,-3,-4,-5] => [1,1,1]
=> 0 = 1 - 1
[1,2,3,5,4] => [-1,-2,-3,-5,-4] => [1,1,1]
=> 0 = 1 - 1
[1,2,3,5,-4] => [-1,-2,-3,-5,4] => [2,1,1,1]
=> 0 = 1 - 1
[1,2,3,-5,4] => [-1,-2,-3,5,-4] => [2,1,1,1]
=> 0 = 1 - 1
[1,2,3,-5,-4] => [-1,-2,-3,5,4] => [1,1,1]
=> 0 = 1 - 1
[1,2,-3,5,4] => [-1,-2,3,-5,-4] => [1,1]
=> 0 = 1 - 1
[1,2,-3,-5,-4] => [-1,-2,3,5,4] => [1,1]
=> 0 = 1 - 1
[1,-2,3,5,4] => [-1,2,-3,-5,-4] => [1,1]
=> 0 = 1 - 1
[1,-2,3,-5,-4] => [-1,2,-3,5,4] => [1,1]
=> 0 = 1 - 1
[-1,2,3,5,4] => [1,-2,-3,-5,-4] => [1,1]
=> 0 = 1 - 1
[-1,2,3,-5,-4] => [1,-2,-3,5,4] => [1,1]
=> 0 = 1 - 1
[1,2,4,3,5] => [-1,-2,-4,-3,-5] => [1,1,1]
=> 0 = 1 - 1
[1,2,4,3,-5] => [-1,-2,-4,-3,5] => [1,1]
=> 0 = 1 - 1
[1,2,4,-3,5] => [-1,-2,-4,3,-5] => [2,1,1,1]
=> 0 = 1 - 1
[1,2,-4,3,5] => [-1,-2,4,-3,-5] => [2,1,1,1]
=> 0 = 1 - 1
[1,2,-4,-3,5] => [-1,-2,4,3,-5] => [1,1,1]
=> 0 = 1 - 1
[1,2,-4,-3,-5] => [-1,-2,4,3,5] => [1,1]
=> 0 = 1 - 1
[-1,3,2,5,4] => [1,-3,-2,-5,-4] => []
=> ? = 2 - 1
[-1,3,2,-5,-4] => [1,-3,-2,5,4] => []
=> ? = 2 - 1
[-1,-3,-2,5,4] => [1,3,2,-5,-4] => []
=> ? = 2 - 1
[-1,-3,-2,-5,-4] => [1,3,2,5,4] => []
=> ? = 2 - 1
[-1,4,5,2,3] => [1,-4,-5,-2,-3] => []
=> ? = 2 - 1
[-1,4,-5,2,-3] => [1,-4,5,-2,3] => []
=> ? = 2 - 1
[-1,-4,5,-2,3] => [1,4,-5,2,-3] => []
=> ? = 2 - 1
[-1,-4,-5,-2,-3] => [1,4,5,2,3] => []
=> ? = 2 - 1
[-1,5,4,3,2] => [1,-5,-4,-3,-2] => []
=> ? = 2 - 1
[-1,5,-4,-3,2] => [1,-5,4,3,-2] => []
=> ? = 2 - 1
[-1,-5,4,3,-2] => [1,5,-4,-3,2] => []
=> ? = 2 - 1
[-1,-5,-4,-3,-2] => [1,5,4,3,2] => []
=> ? = 2 - 1
[2,1,-3,5,4] => [-2,-1,3,-5,-4] => []
=> ? = 2 - 1
[2,1,-3,-5,-4] => [-2,-1,3,5,4] => []
=> ? = 2 - 1
[-2,-1,-3,5,4] => [2,1,3,-5,-4] => []
=> ? = 2 - 1
[-2,-1,-3,-5,-4] => [2,1,3,5,4] => []
=> ? = 2 - 1
[2,1,4,3,-5] => [-2,-1,-4,-3,5] => []
=> ? = 2 - 1
[2,1,-4,-3,-5] => [-2,-1,4,3,5] => []
=> ? = 2 - 1
[-2,-1,4,3,-5] => [2,1,-4,-3,5] => []
=> ? = 2 - 1
[-2,-1,-4,-3,-5] => [2,1,4,3,5] => []
=> ? = 2 - 1
[2,1,5,-4,3] => [-2,-1,-5,4,-3] => []
=> ? = 2 - 1
[2,1,-5,-4,-3] => [-2,-1,5,4,3] => []
=> ? = 2 - 1
[-2,-1,5,-4,3] => [2,1,-5,4,-3] => []
=> ? = 2 - 1
[-2,-1,-5,-4,-3] => [2,1,5,4,3] => []
=> ? = 2 - 1
[3,-2,1,5,4] => [-3,2,-1,-5,-4] => []
=> ? = 2 - 1
[3,-2,1,-5,-4] => [-3,2,-1,5,4] => []
=> ? = 2 - 1
[-3,-2,-1,5,4] => [3,2,1,-5,-4] => []
=> ? = 2 - 1
[-3,-2,-1,-5,-4] => [3,2,1,5,4] => []
=> ? = 2 - 1
[3,4,1,2,-5] => [-3,-4,-1,-2,5] => []
=> ? = 2 - 1
[3,-4,1,-2,-5] => [-3,4,-1,2,5] => []
=> ? = 2 - 1
[-3,4,-1,2,-5] => [3,-4,1,-2,5] => []
=> ? = 2 - 1
[-3,-4,-1,-2,-5] => [3,4,1,2,5] => []
=> ? = 2 - 1
[3,5,1,-4,2] => [-3,-5,-1,4,-2] => []
=> ? = 2 - 1
[3,-5,1,-4,-2] => [-3,5,-1,4,2] => []
=> ? = 2 - 1
[-3,5,-1,-4,2] => [3,-5,1,4,-2] => []
=> ? = 2 - 1
[-3,-5,-1,-4,-2] => [3,5,1,4,2] => []
=> ? = 2 - 1
[4,-2,5,1,3] => [-4,2,-5,-1,-3] => []
=> ? = 2 - 1
[4,-2,-5,1,-3] => [-4,2,5,-1,3] => []
=> ? = 2 - 1
Description
This is the number of standard Young tableaux of the given shifted shape.
For an integer partition $\lambda = (\lambda_1,\dots,\lambda_k)$, the shifted diagram is obtained by moving the $i$-th row in the diagram $i-1$ boxes to the right, i.e.,
$$\lambda^∗ = \{(i, j) | 1 \leq i \leq k, i \leq j \leq \lambda_i + i − 1 \}.$$
In particular, this statistic is zero if and only if $\lambda_{i+1} = \lambda_i$ for some $i$.
Matching statistic: St001283
Mp00244: Signed permutations —bar⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001283: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 43%●distinct values known / distinct values provided: 29%
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001283: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 43%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [-1,-2,-3] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,4] => [-1,-2,-3,-4] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4] => [-1,-2,-3,4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,4] => [-1,-2,3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,4] => [-1,2,-3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,4] => [1,-2,-3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,4,3] => [-1,-2,-4,-3] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,-4,-3] => [-1,-2,4,3] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,3,2,4] => [-1,-3,-2,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-3,-2,4] => [-1,3,2,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,4,3,2] => [-1,-4,-3,-2] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-4,3,-2] => [-1,4,-3,2] => [1,1]
=> [2]
=> 0 = 1 - 1
[2,1,3,4] => [-2,-1,-3,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-2,-1,3,4] => [2,1,-3,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[2,1,4,3] => [-2,-1,-4,-3] => []
=> []
=> ? = 2 - 1
[2,1,-4,-3] => [-2,-1,4,3] => []
=> []
=> ? = 2 - 1
[-2,-1,4,3] => [2,1,-4,-3] => []
=> []
=> ? = 2 - 1
[-2,-1,-4,-3] => [2,1,4,3] => []
=> []
=> ? = 2 - 1
[3,2,1,4] => [-3,-2,-1,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-3,2,-1,4] => [3,-2,1,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[3,4,1,2] => [-3,-4,-1,-2] => []
=> []
=> ? = 2 - 1
[3,-4,1,-2] => [-3,4,-1,2] => []
=> []
=> ? = 2 - 1
[-3,4,-1,2] => [3,-4,1,-2] => []
=> []
=> ? = 2 - 1
[-3,-4,-1,-2] => [3,4,1,2] => []
=> []
=> ? = 2 - 1
[4,2,3,1] => [-4,-2,-3,-1] => [1,1]
=> [2]
=> 0 = 1 - 1
[-4,2,3,-1] => [4,-2,-3,1] => [1,1]
=> [2]
=> 0 = 1 - 1
[4,3,2,1] => [-4,-3,-2,-1] => []
=> []
=> ? = 2 - 1
[4,-3,-2,1] => [-4,3,2,-1] => []
=> []
=> ? = 2 - 1
[-4,3,2,-1] => [4,-3,-2,1] => []
=> []
=> ? = 2 - 1
[-4,-3,-2,-1] => [4,3,2,1] => []
=> []
=> ? = 2 - 1
[1,2,3,4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [5]
=> 0 = 1 - 1
[1,2,3,4,-5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4,5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4,-5] => [-1,-2,-3,4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,4,5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,-3,4,-5] => [-1,-2,3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,-4,5] => [-1,-2,3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,4,5] => [-1,2,-3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,-2,3,4,-5] => [-1,2,-3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,-4,5] => [-1,2,-3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,-3,4,5] => [-1,2,3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[-1,2,3,4,-5] => [1,-2,-3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,-4,5] => [1,-2,-3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,-3,4,5] => [1,-2,3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,-2,3,4,5] => [1,2,-3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,5,4] => [-1,-2,-3,-5,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,5,-4] => [-1,-2,-3,-5,4] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,3,-5,4] => [-1,-2,-3,5,-4] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,3,-5,-4] => [-1,-2,-3,5,4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,5,4] => [-1,-2,3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,-3,-5,-4] => [-1,-2,3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-2,3,5,4] => [-1,2,-3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-2,3,-5,-4] => [-1,2,-3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,2,3,5,4] => [1,-2,-3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,2,3,-5,-4] => [1,-2,-3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,4,3,5] => [-1,-2,-4,-3,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,4,3,-5] => [-1,-2,-4,-3,5] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,4,-3,5] => [-1,-2,-4,3,-5] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,-4,3,5] => [-1,-2,4,-3,-5] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,-4,-3,5] => [-1,-2,4,3,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-4,-3,-5] => [-1,-2,4,3,5] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,3,2,5,4] => [1,-3,-2,-5,-4] => []
=> []
=> ? = 2 - 1
[-1,3,2,-5,-4] => [1,-3,-2,5,4] => []
=> []
=> ? = 2 - 1
[-1,-3,-2,5,4] => [1,3,2,-5,-4] => []
=> []
=> ? = 2 - 1
[-1,-3,-2,-5,-4] => [1,3,2,5,4] => []
=> []
=> ? = 2 - 1
[-1,4,5,2,3] => [1,-4,-5,-2,-3] => []
=> []
=> ? = 2 - 1
[-1,4,-5,2,-3] => [1,-4,5,-2,3] => []
=> []
=> ? = 2 - 1
[-1,-4,5,-2,3] => [1,4,-5,2,-3] => []
=> []
=> ? = 2 - 1
[-1,-4,-5,-2,-3] => [1,4,5,2,3] => []
=> []
=> ? = 2 - 1
[-1,5,4,3,2] => [1,-5,-4,-3,-2] => []
=> []
=> ? = 2 - 1
[-1,5,-4,-3,2] => [1,-5,4,3,-2] => []
=> []
=> ? = 2 - 1
[-1,-5,4,3,-2] => [1,5,-4,-3,2] => []
=> []
=> ? = 2 - 1
[-1,-5,-4,-3,-2] => [1,5,4,3,2] => []
=> []
=> ? = 2 - 1
[2,1,-3,5,4] => [-2,-1,3,-5,-4] => []
=> []
=> ? = 2 - 1
[2,1,-3,-5,-4] => [-2,-1,3,5,4] => []
=> []
=> ? = 2 - 1
[-2,-1,-3,5,4] => [2,1,3,-5,-4] => []
=> []
=> ? = 2 - 1
[-2,-1,-3,-5,-4] => [2,1,3,5,4] => []
=> []
=> ? = 2 - 1
[2,1,4,3,-5] => [-2,-1,-4,-3,5] => []
=> []
=> ? = 2 - 1
[2,1,-4,-3,-5] => [-2,-1,4,3,5] => []
=> []
=> ? = 2 - 1
[-2,-1,4,3,-5] => [2,1,-4,-3,5] => []
=> []
=> ? = 2 - 1
[-2,-1,-4,-3,-5] => [2,1,4,3,5] => []
=> []
=> ? = 2 - 1
[2,1,5,-4,3] => [-2,-1,-5,4,-3] => []
=> []
=> ? = 2 - 1
[2,1,-5,-4,-3] => [-2,-1,5,4,3] => []
=> []
=> ? = 2 - 1
[-2,-1,5,-4,3] => [2,1,-5,4,-3] => []
=> []
=> ? = 2 - 1
[-2,-1,-5,-4,-3] => [2,1,5,4,3] => []
=> []
=> ? = 2 - 1
[3,-2,1,5,4] => [-3,2,-1,-5,-4] => []
=> []
=> ? = 2 - 1
[3,-2,1,-5,-4] => [-3,2,-1,5,4] => []
=> []
=> ? = 2 - 1
[-3,-2,-1,5,4] => [3,2,1,-5,-4] => []
=> []
=> ? = 2 - 1
[-3,-2,-1,-5,-4] => [3,2,1,5,4] => []
=> []
=> ? = 2 - 1
[3,4,1,2,-5] => [-3,-4,-1,-2,5] => []
=> []
=> ? = 2 - 1
[3,-4,1,-2,-5] => [-3,4,-1,2,5] => []
=> []
=> ? = 2 - 1
[-3,4,-1,2,-5] => [3,-4,1,-2,5] => []
=> []
=> ? = 2 - 1
[-3,-4,-1,-2,-5] => [3,4,1,2,5] => []
=> []
=> ? = 2 - 1
[3,5,1,-4,2] => [-3,-5,-1,4,-2] => []
=> []
=> ? = 2 - 1
[3,-5,1,-4,-2] => [-3,5,-1,4,2] => []
=> []
=> ? = 2 - 1
[-3,5,-1,-4,2] => [3,-5,1,4,-2] => []
=> []
=> ? = 2 - 1
[-3,-5,-1,-4,-2] => [3,5,1,4,2] => []
=> []
=> ? = 2 - 1
[4,-2,5,1,3] => [-4,2,-5,-1,-3] => []
=> []
=> ? = 2 - 1
[4,-2,-5,1,-3] => [-4,2,5,-1,3] => []
=> []
=> ? = 2 - 1
Description
The number of finite solvable groups that are realised by the given partition over the complex numbers.
A finite group $G$ is ''realised'' by the partition $(a_1,\dots,a_m)$ if its group algebra over the complex numbers is isomorphic to the direct product of $a_i\times a_i$ matrix rings over the complex numbers.
The smallest partition which does not realise a solvable group, but does realise a finite group, is $(5,4,3,3,1)$.
Matching statistic: St001284
Mp00244: Signed permutations —bar⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001284: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 43%●distinct values known / distinct values provided: 29%
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001284: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 43%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [-1,-2,-3] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,4] => [-1,-2,-3,-4] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4] => [-1,-2,-3,4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,4] => [-1,-2,3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,4] => [-1,2,-3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,4] => [1,-2,-3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,4,3] => [-1,-2,-4,-3] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,-4,-3] => [-1,-2,4,3] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,3,2,4] => [-1,-3,-2,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-3,-2,4] => [-1,3,2,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,4,3,2] => [-1,-4,-3,-2] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-4,3,-2] => [-1,4,-3,2] => [1,1]
=> [2]
=> 0 = 1 - 1
[2,1,3,4] => [-2,-1,-3,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-2,-1,3,4] => [2,1,-3,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[2,1,4,3] => [-2,-1,-4,-3] => []
=> []
=> ? = 2 - 1
[2,1,-4,-3] => [-2,-1,4,3] => []
=> []
=> ? = 2 - 1
[-2,-1,4,3] => [2,1,-4,-3] => []
=> []
=> ? = 2 - 1
[-2,-1,-4,-3] => [2,1,4,3] => []
=> []
=> ? = 2 - 1
[3,2,1,4] => [-3,-2,-1,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-3,2,-1,4] => [3,-2,1,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[3,4,1,2] => [-3,-4,-1,-2] => []
=> []
=> ? = 2 - 1
[3,-4,1,-2] => [-3,4,-1,2] => []
=> []
=> ? = 2 - 1
[-3,4,-1,2] => [3,-4,1,-2] => []
=> []
=> ? = 2 - 1
[-3,-4,-1,-2] => [3,4,1,2] => []
=> []
=> ? = 2 - 1
[4,2,3,1] => [-4,-2,-3,-1] => [1,1]
=> [2]
=> 0 = 1 - 1
[-4,2,3,-1] => [4,-2,-3,1] => [1,1]
=> [2]
=> 0 = 1 - 1
[4,3,2,1] => [-4,-3,-2,-1] => []
=> []
=> ? = 2 - 1
[4,-3,-2,1] => [-4,3,2,-1] => []
=> []
=> ? = 2 - 1
[-4,3,2,-1] => [4,-3,-2,1] => []
=> []
=> ? = 2 - 1
[-4,-3,-2,-1] => [4,3,2,1] => []
=> []
=> ? = 2 - 1
[1,2,3,4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [5]
=> 0 = 1 - 1
[1,2,3,4,-5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4,5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4,-5] => [-1,-2,-3,4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,4,5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,-3,4,-5] => [-1,-2,3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,-4,5] => [-1,-2,3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,4,5] => [-1,2,-3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,-2,3,4,-5] => [-1,2,-3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,-4,5] => [-1,2,-3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,-3,4,5] => [-1,2,3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[-1,2,3,4,-5] => [1,-2,-3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,-4,5] => [1,-2,-3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,-3,4,5] => [1,-2,3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,-2,3,4,5] => [1,2,-3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,5,4] => [-1,-2,-3,-5,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,5,-4] => [-1,-2,-3,-5,4] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,3,-5,4] => [-1,-2,-3,5,-4] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,3,-5,-4] => [-1,-2,-3,5,4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,5,4] => [-1,-2,3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,-3,-5,-4] => [-1,-2,3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-2,3,5,4] => [-1,2,-3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-2,3,-5,-4] => [-1,2,-3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,2,3,5,4] => [1,-2,-3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,2,3,-5,-4] => [1,-2,-3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,4,3,5] => [-1,-2,-4,-3,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,4,3,-5] => [-1,-2,-4,-3,5] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,4,-3,5] => [-1,-2,-4,3,-5] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,-4,3,5] => [-1,-2,4,-3,-5] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,-4,-3,5] => [-1,-2,4,3,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-4,-3,-5] => [-1,-2,4,3,5] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,3,2,5,4] => [1,-3,-2,-5,-4] => []
=> []
=> ? = 2 - 1
[-1,3,2,-5,-4] => [1,-3,-2,5,4] => []
=> []
=> ? = 2 - 1
[-1,-3,-2,5,4] => [1,3,2,-5,-4] => []
=> []
=> ? = 2 - 1
[-1,-3,-2,-5,-4] => [1,3,2,5,4] => []
=> []
=> ? = 2 - 1
[-1,4,5,2,3] => [1,-4,-5,-2,-3] => []
=> []
=> ? = 2 - 1
[-1,4,-5,2,-3] => [1,-4,5,-2,3] => []
=> []
=> ? = 2 - 1
[-1,-4,5,-2,3] => [1,4,-5,2,-3] => []
=> []
=> ? = 2 - 1
[-1,-4,-5,-2,-3] => [1,4,5,2,3] => []
=> []
=> ? = 2 - 1
[-1,5,4,3,2] => [1,-5,-4,-3,-2] => []
=> []
=> ? = 2 - 1
[-1,5,-4,-3,2] => [1,-5,4,3,-2] => []
=> []
=> ? = 2 - 1
[-1,-5,4,3,-2] => [1,5,-4,-3,2] => []
=> []
=> ? = 2 - 1
[-1,-5,-4,-3,-2] => [1,5,4,3,2] => []
=> []
=> ? = 2 - 1
[2,1,-3,5,4] => [-2,-1,3,-5,-4] => []
=> []
=> ? = 2 - 1
[2,1,-3,-5,-4] => [-2,-1,3,5,4] => []
=> []
=> ? = 2 - 1
[-2,-1,-3,5,4] => [2,1,3,-5,-4] => []
=> []
=> ? = 2 - 1
[-2,-1,-3,-5,-4] => [2,1,3,5,4] => []
=> []
=> ? = 2 - 1
[2,1,4,3,-5] => [-2,-1,-4,-3,5] => []
=> []
=> ? = 2 - 1
[2,1,-4,-3,-5] => [-2,-1,4,3,5] => []
=> []
=> ? = 2 - 1
[-2,-1,4,3,-5] => [2,1,-4,-3,5] => []
=> []
=> ? = 2 - 1
[-2,-1,-4,-3,-5] => [2,1,4,3,5] => []
=> []
=> ? = 2 - 1
[2,1,5,-4,3] => [-2,-1,-5,4,-3] => []
=> []
=> ? = 2 - 1
[2,1,-5,-4,-3] => [-2,-1,5,4,3] => []
=> []
=> ? = 2 - 1
[-2,-1,5,-4,3] => [2,1,-5,4,-3] => []
=> []
=> ? = 2 - 1
[-2,-1,-5,-4,-3] => [2,1,5,4,3] => []
=> []
=> ? = 2 - 1
[3,-2,1,5,4] => [-3,2,-1,-5,-4] => []
=> []
=> ? = 2 - 1
[3,-2,1,-5,-4] => [-3,2,-1,5,4] => []
=> []
=> ? = 2 - 1
[-3,-2,-1,5,4] => [3,2,1,-5,-4] => []
=> []
=> ? = 2 - 1
[-3,-2,-1,-5,-4] => [3,2,1,5,4] => []
=> []
=> ? = 2 - 1
[3,4,1,2,-5] => [-3,-4,-1,-2,5] => []
=> []
=> ? = 2 - 1
[3,-4,1,-2,-5] => [-3,4,-1,2,5] => []
=> []
=> ? = 2 - 1
[-3,4,-1,2,-5] => [3,-4,1,-2,5] => []
=> []
=> ? = 2 - 1
[-3,-4,-1,-2,-5] => [3,4,1,2,5] => []
=> []
=> ? = 2 - 1
[3,5,1,-4,2] => [-3,-5,-1,4,-2] => []
=> []
=> ? = 2 - 1
[3,-5,1,-4,-2] => [-3,5,-1,4,2] => []
=> []
=> ? = 2 - 1
[-3,5,-1,-4,2] => [3,-5,1,4,-2] => []
=> []
=> ? = 2 - 1
[-3,-5,-1,-4,-2] => [3,5,1,4,2] => []
=> []
=> ? = 2 - 1
[4,-2,5,1,3] => [-4,2,-5,-1,-3] => []
=> []
=> ? = 2 - 1
[4,-2,-5,1,-3] => [-4,2,5,-1,3] => []
=> []
=> ? = 2 - 1
Description
The number of finite groups that are realised by the given partition over the complex numbers.
A finite group $G$ is 'realised' by the partition $(a_1,...,a_m)$ if its group algebra over the complex numbers is isomorphic to the direct product of $a_i\times a_i$ matrix rings over the complex numbers.
Matching statistic: St000929
Mp00244: Signed permutations —bar⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 37%●distinct values known / distinct values provided: 29%
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 37%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [-1,-2,-3] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,4] => [-1,-2,-3,-4] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4] => [-1,-2,-3,4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,4] => [-1,-2,3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,4] => [-1,2,-3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,4] => [1,-2,-3,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,4,3] => [-1,-2,-4,-3] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,-4,-3] => [-1,-2,4,3] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,3,2,4] => [-1,-3,-2,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-3,-2,4] => [-1,3,2,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,4,3,2] => [-1,-4,-3,-2] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-4,3,-2] => [-1,4,-3,2] => [1,1]
=> [2]
=> 0 = 1 - 1
[2,1,3,4] => [-2,-1,-3,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-2,-1,3,4] => [2,1,-3,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[2,1,4,3] => [-2,-1,-4,-3] => []
=> []
=> ? = 2 - 1
[2,1,-4,-3] => [-2,-1,4,3] => []
=> []
=> ? = 2 - 1
[-2,-1,4,3] => [2,1,-4,-3] => []
=> []
=> ? = 2 - 1
[-2,-1,-4,-3] => [2,1,4,3] => []
=> []
=> ? = 2 - 1
[3,2,1,4] => [-3,-2,-1,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-3,2,-1,4] => [3,-2,1,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[3,4,1,2] => [-3,-4,-1,-2] => []
=> []
=> ? = 2 - 1
[3,-4,1,-2] => [-3,4,-1,2] => []
=> []
=> ? = 2 - 1
[-3,4,-1,2] => [3,-4,1,-2] => []
=> []
=> ? = 2 - 1
[-3,-4,-1,-2] => [3,4,1,2] => []
=> []
=> ? = 2 - 1
[4,2,3,1] => [-4,-2,-3,-1] => [1,1]
=> [2]
=> 0 = 1 - 1
[-4,2,3,-1] => [4,-2,-3,1] => [1,1]
=> [2]
=> 0 = 1 - 1
[4,3,2,1] => [-4,-3,-2,-1] => []
=> []
=> ? = 2 - 1
[4,-3,-2,1] => [-4,3,2,-1] => []
=> []
=> ? = 2 - 1
[-4,3,2,-1] => [4,-3,-2,1] => []
=> []
=> ? = 2 - 1
[-4,-3,-2,-1] => [4,3,2,1] => []
=> []
=> ? = 2 - 1
[1,2,3,4,5] => [-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [5]
=> 0 = 1 - 1
[1,2,3,4,-5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4,5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,3,-4,-5] => [-1,-2,-3,4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,4,5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,2,-3,4,-5] => [-1,-2,3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,-4,5] => [-1,-2,3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,4,5] => [-1,2,-3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[1,-2,3,4,-5] => [-1,2,-3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,3,-4,5] => [-1,2,-3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,-2,-3,4,5] => [-1,2,3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [4]
=> 0 = 1 - 1
[-1,2,3,4,-5] => [1,-2,-3,-4,5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,3,-4,5] => [1,-2,-3,4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,2,-3,4,5] => [1,-2,3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[-1,-2,3,4,5] => [1,2,-3,-4,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,5,4] => [-1,-2,-3,-5,-4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,3,5,-4] => [-1,-2,-3,-5,4] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,3,-5,4] => [-1,-2,-3,5,-4] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,3,-5,-4] => [-1,-2,-3,5,4] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-3,5,4] => [-1,-2,3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,-3,-5,-4] => [-1,-2,3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-2,3,5,4] => [-1,2,-3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,-2,3,-5,-4] => [-1,2,-3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,2,3,5,4] => [1,-2,-3,-5,-4] => [1,1]
=> [2]
=> 0 = 1 - 1
[-1,2,3,-5,-4] => [1,-2,-3,5,4] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,4,3,5] => [-1,-2,-4,-3,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,4,3,-5] => [-1,-2,-4,-3,5] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,2,4,-3,5] => [-1,-2,-4,3,-5] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,-4,3,5] => [-1,-2,4,-3,-5] => [2,1,1,1]
=> [4,1]
=> 0 = 1 - 1
[1,2,-4,-3,5] => [-1,-2,4,3,-5] => [1,1,1]
=> [3]
=> 0 = 1 - 1
[1,2,-4,-3,-5] => [-1,-2,4,3,5] => [1,1]
=> [2]
=> 0 = 1 - 1
[1,3,2,5,4] => [-1,-3,-2,-5,-4] => [1]
=> [1]
=> ? = 2 - 1
[1,3,2,-5,-4] => [-1,-3,-2,5,4] => [1]
=> [1]
=> ? = 2 - 1
[1,-3,-2,5,4] => [-1,3,2,-5,-4] => [1]
=> [1]
=> ? = 2 - 1
[1,-3,-2,-5,-4] => [-1,3,2,5,4] => [1]
=> [1]
=> ? = 2 - 1
[-1,3,2,5,4] => [1,-3,-2,-5,-4] => []
=> []
=> ? = 2 - 1
[-1,3,2,-5,-4] => [1,-3,-2,5,4] => []
=> []
=> ? = 2 - 1
[-1,-3,-2,5,4] => [1,3,2,-5,-4] => []
=> []
=> ? = 2 - 1
[-1,-3,-2,-5,-4] => [1,3,2,5,4] => []
=> []
=> ? = 2 - 1
[1,4,5,2,3] => [-1,-4,-5,-2,-3] => [1]
=> [1]
=> ? = 2 - 1
[1,4,-5,2,-3] => [-1,-4,5,-2,3] => [1]
=> [1]
=> ? = 2 - 1
[1,-4,5,-2,3] => [-1,4,-5,2,-3] => [1]
=> [1]
=> ? = 2 - 1
[1,-4,-5,-2,-3] => [-1,4,5,2,3] => [1]
=> [1]
=> ? = 2 - 1
[-1,4,5,2,3] => [1,-4,-5,-2,-3] => []
=> []
=> ? = 2 - 1
[-1,4,-5,2,-3] => [1,-4,5,-2,3] => []
=> []
=> ? = 2 - 1
[-1,-4,5,-2,3] => [1,4,-5,2,-3] => []
=> []
=> ? = 2 - 1
[-1,-4,-5,-2,-3] => [1,4,5,2,3] => []
=> []
=> ? = 2 - 1
[1,5,4,3,2] => [-1,-5,-4,-3,-2] => [1]
=> [1]
=> ? = 2 - 1
[1,5,-4,-3,2] => [-1,-5,4,3,-2] => [1]
=> [1]
=> ? = 2 - 1
[1,-5,4,3,-2] => [-1,5,-4,-3,2] => [1]
=> [1]
=> ? = 2 - 1
[1,-5,-4,-3,-2] => [-1,5,4,3,2] => [1]
=> [1]
=> ? = 2 - 1
[-1,5,4,3,2] => [1,-5,-4,-3,-2] => []
=> []
=> ? = 2 - 1
[-1,5,-4,-3,2] => [1,-5,4,3,-2] => []
=> []
=> ? = 2 - 1
[-1,-5,4,3,-2] => [1,5,-4,-3,2] => []
=> []
=> ? = 2 - 1
[-1,-5,-4,-3,-2] => [1,5,4,3,2] => []
=> []
=> ? = 2 - 1
[2,1,3,5,4] => [-2,-1,-3,-5,-4] => [1]
=> [1]
=> ? = 2 - 1
[2,1,3,-5,-4] => [-2,-1,-3,5,4] => [1]
=> [1]
=> ? = 2 - 1
[2,1,-3,5,4] => [-2,-1,3,-5,-4] => []
=> []
=> ? = 2 - 1
[2,1,-3,-5,-4] => [-2,-1,3,5,4] => []
=> []
=> ? = 2 - 1
[-2,-1,3,5,4] => [2,1,-3,-5,-4] => [1]
=> [1]
=> ? = 2 - 1
[-2,-1,3,-5,-4] => [2,1,-3,5,4] => [1]
=> [1]
=> ? = 2 - 1
[-2,-1,-3,5,4] => [2,1,3,-5,-4] => []
=> []
=> ? = 2 - 1
[-2,-1,-3,-5,-4] => [2,1,3,5,4] => []
=> []
=> ? = 2 - 1
[2,1,4,3,5] => [-2,-1,-4,-3,-5] => [1]
=> [1]
=> ? = 2 - 1
[2,1,4,3,-5] => [-2,-1,-4,-3,5] => []
=> []
=> ? = 2 - 1
[2,1,-4,-3,5] => [-2,-1,4,3,-5] => [1]
=> [1]
=> ? = 2 - 1
[2,1,-4,-3,-5] => [-2,-1,4,3,5] => []
=> []
=> ? = 2 - 1
[-2,-1,4,3,5] => [2,1,-4,-3,-5] => [1]
=> [1]
=> ? = 2 - 1
[-2,-1,4,3,-5] => [2,1,-4,-3,5] => []
=> []
=> ? = 2 - 1
Description
The constant term of the character polynomial of an integer partition.
The definition of the character polynomial can be found in [1]. Indeed, this constant term is $0$ for partitions $\lambda \neq 1^n$ and $1$ for $\lambda = 1^n$.
Matching statistic: St001604
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00244: Signed permutations —bar⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 29%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [-1,-2,-3] => []
=> ? = 1 - 1
[1,2,3,4] => [-1,-2,-3,-4] => []
=> ? = 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
[-1,2,3,4] => [1,-2,-3,-4] => [1]
=> ? = 1 - 1
[1,2,4,3] => [-1,-2,-4,-3] => [2]
=> ? = 1 - 1
[1,2,-4,-3] => [-1,-2,4,3] => [2]
=> ? = 1 - 1
[1,3,2,4] => [-1,-3,-2,-4] => [2]
=> ? = 1 - 1
[1,-3,-2,4] => [-1,3,2,-4] => [2]
=> ? = 1 - 1
[1,4,3,2] => [-1,-4,-3,-2] => [2]
=> ? = 1 - 1
[1,-4,3,-2] => [-1,4,-3,2] => [2]
=> ? = 1 - 1
[2,1,3,4] => [-2,-1,-3,-4] => [2]
=> ? = 1 - 1
[-2,-1,3,4] => [2,1,-3,-4] => [2]
=> ? = 1 - 1
[2,1,4,3] => [-2,-1,-4,-3] => [2,2]
=> 1 = 2 - 1
[2,1,-4,-3] => [-2,-1,4,3] => [2,2]
=> 1 = 2 - 1
[-2,-1,4,3] => [2,1,-4,-3] => [2,2]
=> 1 = 2 - 1
[-2,-1,-4,-3] => [2,1,4,3] => [2,2]
=> 1 = 2 - 1
[3,2,1,4] => [-3,-2,-1,-4] => [2]
=> ? = 1 - 1
[-3,2,-1,4] => [3,-2,1,-4] => [2]
=> ? = 1 - 1
[3,4,1,2] => [-3,-4,-1,-2] => [2,2]
=> 1 = 2 - 1
[3,-4,1,-2] => [-3,4,-1,2] => [2,2]
=> 1 = 2 - 1
[-3,4,-1,2] => [3,-4,1,-2] => [2,2]
=> 1 = 2 - 1
[-3,-4,-1,-2] => [3,4,1,2] => [2,2]
=> 1 = 2 - 1
[4,2,3,1] => [-4,-2,-3,-1] => [2]
=> ? = 1 - 1
[-4,2,3,-1] => [4,-2,-3,1] => [2]
=> ? = 1 - 1
[4,3,2,1] => [-4,-3,-2,-1] => [2,2]
=> 1 = 2 - 1
[4,-3,-2,1] => [-4,3,2,-1] => [2,2]
=> 1 = 2 - 1
[-4,3,2,-1] => [4,-3,-2,1] => [2,2]
=> 1 = 2 - 1
[-4,-3,-2,-1] => [4,3,2,1] => [2,2]
=> 1 = 2 - 1
[1,2,3,4,5] => [-1,-2,-3,-4,-5] => []
=> ? = 1 - 1
[1,2,3,4,-5] => [-1,-2,-3,-4,5] => [1]
=> ? = 1 - 1
[1,2,3,-4,5] => [-1,-2,-3,4,-5] => [1]
=> ? = 1 - 1
[1,2,3,-4,-5] => [-1,-2,-3,4,5] => [1,1]
=> ? = 1 - 1
[1,2,-3,4,5] => [-1,-2,3,-4,-5] => [1]
=> ? = 1 - 1
[1,2,-3,4,-5] => [-1,-2,3,-4,5] => [1,1]
=> ? = 1 - 1
[1,2,-3,-4,5] => [-1,-2,3,4,-5] => [1,1]
=> ? = 1 - 1
[1,-2,3,4,5] => [-1,2,-3,-4,-5] => [1]
=> ? = 1 - 1
[1,-2,3,4,-5] => [-1,2,-3,-4,5] => [1,1]
=> ? = 1 - 1
[1,-2,3,-4,5] => [-1,2,-3,4,-5] => [1,1]
=> ? = 1 - 1
[1,-2,-3,4,5] => [-1,2,3,-4,-5] => [1,1]
=> ? = 1 - 1
[-1,2,3,4,5] => [1,-2,-3,-4,-5] => [1]
=> ? = 1 - 1
[-1,2,3,4,-5] => [1,-2,-3,-4,5] => [1,1]
=> ? = 1 - 1
[-1,2,3,-4,5] => [1,-2,-3,4,-5] => [1,1]
=> ? = 1 - 1
[-1,2,-3,4,5] => [1,-2,3,-4,-5] => [1,1]
=> ? = 1 - 1
[-1,-2,3,4,5] => [1,2,-3,-4,-5] => [1,1]
=> ? = 1 - 1
[1,2,3,5,4] => [-1,-2,-3,-5,-4] => [2]
=> ? = 1 - 1
[1,2,3,5,-4] => [-1,-2,-3,-5,4] => []
=> ? = 1 - 1
[1,2,3,-5,4] => [-1,-2,-3,5,-4] => []
=> ? = 1 - 1
[1,2,3,-5,-4] => [-1,-2,-3,5,4] => [2]
=> ? = 1 - 1
[1,2,-3,5,4] => [-1,-2,3,-5,-4] => [2,1]
=> 0 = 1 - 1
[1,2,-3,-5,-4] => [-1,-2,3,5,4] => [2,1]
=> 0 = 1 - 1
[1,-2,3,5,4] => [-1,2,-3,-5,-4] => [2,1]
=> 0 = 1 - 1
[1,-2,3,-5,-4] => [-1,2,-3,5,4] => [2,1]
=> 0 = 1 - 1
[-1,2,3,5,4] => [1,-2,-3,-5,-4] => [2,1]
=> 0 = 1 - 1
[-1,2,3,-5,-4] => [1,-2,-3,5,4] => [2,1]
=> 0 = 1 - 1
[1,2,4,3,5] => [-1,-2,-4,-3,-5] => [2]
=> ? = 1 - 1
[1,2,4,3,-5] => [-1,-2,-4,-3,5] => [2,1]
=> 0 = 1 - 1
[1,2,4,-3,5] => [-1,-2,-4,3,-5] => []
=> ? = 1 - 1
[1,2,-4,3,5] => [-1,-2,4,-3,-5] => []
=> ? = 1 - 1
[1,2,-4,-3,5] => [-1,-2,4,3,-5] => [2]
=> ? = 1 - 1
[1,2,-4,-3,-5] => [-1,-2,4,3,5] => [2,1]
=> 0 = 1 - 1
[1,-2,4,3,5] => [-1,2,-4,-3,-5] => [2,1]
=> 0 = 1 - 1
[1,-2,-4,-3,5] => [-1,2,4,3,-5] => [2,1]
=> 0 = 1 - 1
[-1,2,4,3,5] => [1,-2,-4,-3,-5] => [2,1]
=> 0 = 1 - 1
[-1,2,-4,-3,5] => [1,-2,4,3,-5] => [2,1]
=> 0 = 1 - 1
[1,2,4,5,3] => [-1,-2,-4,-5,-3] => []
=> ? = 1 - 1
[1,2,4,-5,-3] => [-1,-2,-4,5,3] => []
=> ? = 1 - 1
[1,2,-4,5,-3] => [-1,-2,4,-5,3] => []
=> ? = 1 - 1
[1,2,-4,-5,3] => [-1,-2,4,5,-3] => []
=> ? = 1 - 1
[1,2,5,3,4] => [-1,-2,-5,-3,-4] => []
=> ? = 1 - 1
[1,2,5,-3,-4] => [-1,-2,-5,3,4] => []
=> ? = 1 - 1
[1,2,-5,3,-4] => [-1,-2,5,-3,4] => []
=> ? = 1 - 1
[1,2,-5,-3,4] => [-1,-2,5,3,-4] => []
=> ? = 1 - 1
[1,2,5,-4,3] => [-1,-2,-5,4,-3] => [2,1]
=> 0 = 1 - 1
[1,2,-5,-4,-3] => [-1,-2,5,4,3] => [2,1]
=> 0 = 1 - 1
[1,-2,5,4,3] => [-1,2,-5,-4,-3] => [2,1]
=> 0 = 1 - 1
[1,-2,-5,4,-3] => [-1,2,5,-4,3] => [2,1]
=> 0 = 1 - 1
[-1,2,5,4,3] => [1,-2,-5,-4,-3] => [2,1]
=> 0 = 1 - 1
[-1,2,-5,4,-3] => [1,-2,5,-4,3] => [2,1]
=> 0 = 1 - 1
[1,3,2,4,-5] => [-1,-3,-2,-4,5] => [2,1]
=> 0 = 1 - 1
[1,3,2,-4,5] => [-1,-3,-2,4,-5] => [2,1]
=> 0 = 1 - 1
[1,-3,-2,4,-5] => [-1,3,2,-4,5] => [2,1]
=> 0 = 1 - 1
[1,-3,-2,-4,5] => [-1,3,2,4,-5] => [2,1]
=> 0 = 1 - 1
[-1,3,2,4,5] => [1,-3,-2,-4,-5] => [2,1]
=> 0 = 1 - 1
[-1,-3,-2,4,5] => [1,3,2,-4,-5] => [2,1]
=> 0 = 1 - 1
[1,3,2,5,4] => [-1,-3,-2,-5,-4] => [2,2]
=> 1 = 2 - 1
[1,3,2,-5,-4] => [-1,-3,-2,5,4] => [2,2]
=> 1 = 2 - 1
[1,-3,-2,5,4] => [-1,3,2,-5,-4] => [2,2]
=> 1 = 2 - 1
[1,-3,-2,-5,-4] => [-1,3,2,5,4] => [2,2]
=> 1 = 2 - 1
[-1,3,2,5,4] => [1,-3,-2,-5,-4] => [2,2,1]
=> 1 = 2 - 1
[-1,3,2,-5,-4] => [1,-3,-2,5,4] => [2,2,1]
=> 1 = 2 - 1
[-1,-3,-2,5,4] => [1,3,2,-5,-4] => [2,2,1]
=> 1 = 2 - 1
[-1,-3,-2,-5,-4] => [1,3,2,5,4] => [2,2,1]
=> 1 = 2 - 1
[1,4,3,2,-5] => [-1,-4,-3,-2,5] => [2,1]
=> 0 = 1 - 1
[1,4,-3,2,5] => [-1,-4,3,-2,-5] => [2,1]
=> 0 = 1 - 1
[1,-4,3,-2,-5] => [-1,4,-3,2,5] => [2,1]
=> 0 = 1 - 1
[1,-4,-3,-2,5] => [-1,4,3,2,-5] => [2,1]
=> 0 = 1 - 1
[-1,4,3,2,5] => [1,-4,-3,-2,-5] => [2,1]
=> 0 = 1 - 1
[-1,-4,3,-2,5] => [1,4,-3,2,-5] => [2,1]
=> 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: St001603
Mp00244: Signed permutations —bar⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 29%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [-1,-2,-3] => []
=> []
=> ? = 1
[1,2,3,4] => [-1,-2,-3,-4] => []
=> []
=> ? = 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
[1,2,4,3] => [-1,-2,-4,-3] => [2]
=> [1,1]
=> ? = 1
[1,2,-4,-3] => [-1,-2,4,3] => [2]
=> [1,1]
=> ? = 1
[1,3,2,4] => [-1,-3,-2,-4] => [2]
=> [1,1]
=> ? = 1
[1,-3,-2,4] => [-1,3,2,-4] => [2]
=> [1,1]
=> ? = 1
[1,4,3,2] => [-1,-4,-3,-2] => [2]
=> [1,1]
=> ? = 1
[1,-4,3,-2] => [-1,4,-3,2] => [2]
=> [1,1]
=> ? = 1
[2,1,3,4] => [-2,-1,-3,-4] => [2]
=> [1,1]
=> ? = 1
[-2,-1,3,4] => [2,1,-3,-4] => [2]
=> [1,1]
=> ? = 1
[2,1,4,3] => [-2,-1,-4,-3] => [2,2]
=> [2,2]
=> 2
[2,1,-4,-3] => [-2,-1,4,3] => [2,2]
=> [2,2]
=> 2
[-2,-1,4,3] => [2,1,-4,-3] => [2,2]
=> [2,2]
=> 2
[-2,-1,-4,-3] => [2,1,4,3] => [2,2]
=> [2,2]
=> 2
[3,2,1,4] => [-3,-2,-1,-4] => [2]
=> [1,1]
=> ? = 1
[-3,2,-1,4] => [3,-2,1,-4] => [2]
=> [1,1]
=> ? = 1
[3,4,1,2] => [-3,-4,-1,-2] => [2,2]
=> [2,2]
=> 2
[3,-4,1,-2] => [-3,4,-1,2] => [2,2]
=> [2,2]
=> 2
[-3,4,-1,2] => [3,-4,1,-2] => [2,2]
=> [2,2]
=> 2
[-3,-4,-1,-2] => [3,4,1,2] => [2,2]
=> [2,2]
=> 2
[4,2,3,1] => [-4,-2,-3,-1] => [2]
=> [1,1]
=> ? = 1
[-4,2,3,-1] => [4,-2,-3,1] => [2]
=> [1,1]
=> ? = 1
[4,3,2,1] => [-4,-3,-2,-1] => [2,2]
=> [2,2]
=> 2
[4,-3,-2,1] => [-4,3,2,-1] => [2,2]
=> [2,2]
=> 2
[-4,3,2,-1] => [4,-3,-2,1] => [2,2]
=> [2,2]
=> 2
[-4,-3,-2,-1] => [4,3,2,1] => [2,2]
=> [2,2]
=> 2
[1,2,3,4,5] => [-1,-2,-3,-4,-5] => []
=> []
=> ? = 1
[1,2,3,4,-5] => [-1,-2,-3,-4,5] => [1]
=> [1]
=> ? = 1
[1,2,3,-4,5] => [-1,-2,-3,4,-5] => [1]
=> [1]
=> ? = 1
[1,2,3,-4,-5] => [-1,-2,-3,4,5] => [1,1]
=> [2]
=> ? = 1
[1,2,-3,4,5] => [-1,-2,3,-4,-5] => [1]
=> [1]
=> ? = 1
[1,2,-3,4,-5] => [-1,-2,3,-4,5] => [1,1]
=> [2]
=> ? = 1
[1,2,-3,-4,5] => [-1,-2,3,4,-5] => [1,1]
=> [2]
=> ? = 1
[1,-2,3,4,5] => [-1,2,-3,-4,-5] => [1]
=> [1]
=> ? = 1
[1,-2,3,4,-5] => [-1,2,-3,-4,5] => [1,1]
=> [2]
=> ? = 1
[1,-2,3,-4,5] => [-1,2,-3,4,-5] => [1,1]
=> [2]
=> ? = 1
[1,-2,-3,4,5] => [-1,2,3,-4,-5] => [1,1]
=> [2]
=> ? = 1
[-1,2,3,4,5] => [1,-2,-3,-4,-5] => [1]
=> [1]
=> ? = 1
[-1,2,3,4,-5] => [1,-2,-3,-4,5] => [1,1]
=> [2]
=> ? = 1
[-1,2,3,-4,5] => [1,-2,-3,4,-5] => [1,1]
=> [2]
=> ? = 1
[-1,2,-3,4,5] => [1,-2,3,-4,-5] => [1,1]
=> [2]
=> ? = 1
[-1,-2,3,4,5] => [1,2,-3,-4,-5] => [1,1]
=> [2]
=> ? = 1
[1,2,3,5,4] => [-1,-2,-3,-5,-4] => [2]
=> [1,1]
=> ? = 1
[1,2,3,5,-4] => [-1,-2,-3,-5,4] => []
=> []
=> ? = 1
[1,2,3,-5,4] => [-1,-2,-3,5,-4] => []
=> []
=> ? = 1
[1,2,3,-5,-4] => [-1,-2,-3,5,4] => [2]
=> [1,1]
=> ? = 1
[1,2,-3,5,4] => [-1,-2,3,-5,-4] => [2,1]
=> [2,1]
=> 1
[1,2,-3,-5,-4] => [-1,-2,3,5,4] => [2,1]
=> [2,1]
=> 1
[1,-2,3,5,4] => [-1,2,-3,-5,-4] => [2,1]
=> [2,1]
=> 1
[1,-2,3,-5,-4] => [-1,2,-3,5,4] => [2,1]
=> [2,1]
=> 1
[-1,2,3,5,4] => [1,-2,-3,-5,-4] => [2,1]
=> [2,1]
=> 1
[-1,2,3,-5,-4] => [1,-2,-3,5,4] => [2,1]
=> [2,1]
=> 1
[1,2,4,3,5] => [-1,-2,-4,-3,-5] => [2]
=> [1,1]
=> ? = 1
[1,2,4,3,-5] => [-1,-2,-4,-3,5] => [2,1]
=> [2,1]
=> 1
[1,2,4,-3,5] => [-1,-2,-4,3,-5] => []
=> []
=> ? = 1
[1,2,-4,3,5] => [-1,-2,4,-3,-5] => []
=> []
=> ? = 1
[1,2,-4,-3,5] => [-1,-2,4,3,-5] => [2]
=> [1,1]
=> ? = 1
[1,2,-4,-3,-5] => [-1,-2,4,3,5] => [2,1]
=> [2,1]
=> 1
[1,-2,4,3,5] => [-1,2,-4,-3,-5] => [2,1]
=> [2,1]
=> 1
[1,-2,-4,-3,5] => [-1,2,4,3,-5] => [2,1]
=> [2,1]
=> 1
[-1,2,4,3,5] => [1,-2,-4,-3,-5] => [2,1]
=> [2,1]
=> 1
[-1,2,-4,-3,5] => [1,-2,4,3,-5] => [2,1]
=> [2,1]
=> 1
[1,2,4,5,3] => [-1,-2,-4,-5,-3] => []
=> []
=> ? = 1
[1,2,4,-5,-3] => [-1,-2,-4,5,3] => []
=> []
=> ? = 1
[1,2,-4,5,-3] => [-1,-2,4,-5,3] => []
=> []
=> ? = 1
[1,2,-4,-5,3] => [-1,-2,4,5,-3] => []
=> []
=> ? = 1
[1,2,5,3,4] => [-1,-2,-5,-3,-4] => []
=> []
=> ? = 1
[1,2,5,-3,-4] => [-1,-2,-5,3,4] => []
=> []
=> ? = 1
[1,2,-5,3,-4] => [-1,-2,5,-3,4] => []
=> []
=> ? = 1
[1,2,-5,-3,4] => [-1,-2,5,3,-4] => []
=> []
=> ? = 1
[1,2,5,-4,3] => [-1,-2,-5,4,-3] => [2,1]
=> [2,1]
=> 1
[1,2,-5,-4,-3] => [-1,-2,5,4,3] => [2,1]
=> [2,1]
=> 1
[1,-2,5,4,3] => [-1,2,-5,-4,-3] => [2,1]
=> [2,1]
=> 1
[1,-2,-5,4,-3] => [-1,2,5,-4,3] => [2,1]
=> [2,1]
=> 1
[-1,2,5,4,3] => [1,-2,-5,-4,-3] => [2,1]
=> [2,1]
=> 1
[-1,2,-5,4,-3] => [1,-2,5,-4,3] => [2,1]
=> [2,1]
=> 1
[1,3,2,4,-5] => [-1,-3,-2,-4,5] => [2,1]
=> [2,1]
=> 1
[1,3,2,-4,5] => [-1,-3,-2,4,-5] => [2,1]
=> [2,1]
=> 1
[1,-3,-2,4,-5] => [-1,3,2,-4,5] => [2,1]
=> [2,1]
=> 1
[1,-3,-2,-4,5] => [-1,3,2,4,-5] => [2,1]
=> [2,1]
=> 1
[-1,3,2,4,5] => [1,-3,-2,-4,-5] => [2,1]
=> [2,1]
=> 1
[-1,-3,-2,4,5] => [1,3,2,-4,-5] => [2,1]
=> [2,1]
=> 1
[1,3,2,5,4] => [-1,-3,-2,-5,-4] => [2,2]
=> [2,2]
=> 2
[1,3,2,-5,-4] => [-1,-3,-2,5,4] => [2,2]
=> [2,2]
=> 2
[1,-3,-2,5,4] => [-1,3,2,-5,-4] => [2,2]
=> [2,2]
=> 2
[1,-3,-2,-5,-4] => [-1,3,2,5,4] => [2,2]
=> [2,2]
=> 2
[-1,3,2,5,4] => [1,-3,-2,-5,-4] => [2,2,1]
=> [3,2]
=> 2
[-1,3,2,-5,-4] => [1,-3,-2,5,4] => [2,2,1]
=> [3,2]
=> 2
[-1,-3,-2,5,4] => [1,3,2,-5,-4] => [2,2,1]
=> [3,2]
=> 2
[-1,-3,-2,-5,-4] => [1,3,2,5,4] => [2,2,1]
=> [3,2]
=> 2
[1,4,3,2,-5] => [-1,-4,-3,-2,5] => [2,1]
=> [2,1]
=> 1
[1,4,-3,2,5] => [-1,-4,3,-2,-5] => [2,1]
=> [2,1]
=> 1
[1,-4,3,-2,-5] => [-1,4,-3,2,5] => [2,1]
=> [2,1]
=> 1
[1,-4,-3,-2,5] => [-1,4,3,2,-5] => [2,1]
=> [2,1]
=> 1
[-1,4,3,2,5] => [1,-4,-3,-2,-5] => [2,1]
=> [2,1]
=> 1
[-1,-4,3,-2,5] => [1,4,-3,2,-5] => [2,1]
=> [2,1]
=> 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: St001605
Mp00244: Signed permutations —bar⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 29%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [-1,-2,-3] => []
=> []
=> ? = 1
[1,2,3,4] => [-1,-2,-3,-4] => []
=> []
=> ? = 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
[1,2,4,3] => [-1,-2,-4,-3] => [2]
=> [1,1]
=> ? = 1
[1,2,-4,-3] => [-1,-2,4,3] => [2]
=> [1,1]
=> ? = 1
[1,3,2,4] => [-1,-3,-2,-4] => [2]
=> [1,1]
=> ? = 1
[1,-3,-2,4] => [-1,3,2,-4] => [2]
=> [1,1]
=> ? = 1
[1,4,3,2] => [-1,-4,-3,-2] => [2]
=> [1,1]
=> ? = 1
[1,-4,3,-2] => [-1,4,-3,2] => [2]
=> [1,1]
=> ? = 1
[2,1,3,4] => [-2,-1,-3,-4] => [2]
=> [1,1]
=> ? = 1
[-2,-1,3,4] => [2,1,-3,-4] => [2]
=> [1,1]
=> ? = 1
[2,1,4,3] => [-2,-1,-4,-3] => [2,2]
=> [2,2]
=> 2
[2,1,-4,-3] => [-2,-1,4,3] => [2,2]
=> [2,2]
=> 2
[-2,-1,4,3] => [2,1,-4,-3] => [2,2]
=> [2,2]
=> 2
[-2,-1,-4,-3] => [2,1,4,3] => [2,2]
=> [2,2]
=> 2
[3,2,1,4] => [-3,-2,-1,-4] => [2]
=> [1,1]
=> ? = 1
[-3,2,-1,4] => [3,-2,1,-4] => [2]
=> [1,1]
=> ? = 1
[3,4,1,2] => [-3,-4,-1,-2] => [2,2]
=> [2,2]
=> 2
[3,-4,1,-2] => [-3,4,-1,2] => [2,2]
=> [2,2]
=> 2
[-3,4,-1,2] => [3,-4,1,-2] => [2,2]
=> [2,2]
=> 2
[-3,-4,-1,-2] => [3,4,1,2] => [2,2]
=> [2,2]
=> 2
[4,2,3,1] => [-4,-2,-3,-1] => [2]
=> [1,1]
=> ? = 1
[-4,2,3,-1] => [4,-2,-3,1] => [2]
=> [1,1]
=> ? = 1
[4,3,2,1] => [-4,-3,-2,-1] => [2,2]
=> [2,2]
=> 2
[4,-3,-2,1] => [-4,3,2,-1] => [2,2]
=> [2,2]
=> 2
[-4,3,2,-1] => [4,-3,-2,1] => [2,2]
=> [2,2]
=> 2
[-4,-3,-2,-1] => [4,3,2,1] => [2,2]
=> [2,2]
=> 2
[1,2,3,4,5] => [-1,-2,-3,-4,-5] => []
=> []
=> ? = 1
[1,2,3,4,-5] => [-1,-2,-3,-4,5] => [1]
=> [1]
=> ? = 1
[1,2,3,-4,5] => [-1,-2,-3,4,-5] => [1]
=> [1]
=> ? = 1
[1,2,3,-4,-5] => [-1,-2,-3,4,5] => [1,1]
=> [2]
=> ? = 1
[1,2,-3,4,5] => [-1,-2,3,-4,-5] => [1]
=> [1]
=> ? = 1
[1,2,-3,4,-5] => [-1,-2,3,-4,5] => [1,1]
=> [2]
=> ? = 1
[1,2,-3,-4,5] => [-1,-2,3,4,-5] => [1,1]
=> [2]
=> ? = 1
[1,-2,3,4,5] => [-1,2,-3,-4,-5] => [1]
=> [1]
=> ? = 1
[1,-2,3,4,-5] => [-1,2,-3,-4,5] => [1,1]
=> [2]
=> ? = 1
[1,-2,3,-4,5] => [-1,2,-3,4,-5] => [1,1]
=> [2]
=> ? = 1
[1,-2,-3,4,5] => [-1,2,3,-4,-5] => [1,1]
=> [2]
=> ? = 1
[-1,2,3,4,5] => [1,-2,-3,-4,-5] => [1]
=> [1]
=> ? = 1
[-1,2,3,4,-5] => [1,-2,-3,-4,5] => [1,1]
=> [2]
=> ? = 1
[-1,2,3,-4,5] => [1,-2,-3,4,-5] => [1,1]
=> [2]
=> ? = 1
[-1,2,-3,4,5] => [1,-2,3,-4,-5] => [1,1]
=> [2]
=> ? = 1
[-1,-2,3,4,5] => [1,2,-3,-4,-5] => [1,1]
=> [2]
=> ? = 1
[1,2,3,5,4] => [-1,-2,-3,-5,-4] => [2]
=> [1,1]
=> ? = 1
[1,2,3,5,-4] => [-1,-2,-3,-5,4] => []
=> []
=> ? = 1
[1,2,3,-5,4] => [-1,-2,-3,5,-4] => []
=> []
=> ? = 1
[1,2,3,-5,-4] => [-1,-2,-3,5,4] => [2]
=> [1,1]
=> ? = 1
[1,2,-3,5,4] => [-1,-2,3,-5,-4] => [2,1]
=> [2,1]
=> 1
[1,2,-3,-5,-4] => [-1,-2,3,5,4] => [2,1]
=> [2,1]
=> 1
[1,-2,3,5,4] => [-1,2,-3,-5,-4] => [2,1]
=> [2,1]
=> 1
[1,-2,3,-5,-4] => [-1,2,-3,5,4] => [2,1]
=> [2,1]
=> 1
[-1,2,3,5,4] => [1,-2,-3,-5,-4] => [2,1]
=> [2,1]
=> 1
[-1,2,3,-5,-4] => [1,-2,-3,5,4] => [2,1]
=> [2,1]
=> 1
[1,2,4,3,5] => [-1,-2,-4,-3,-5] => [2]
=> [1,1]
=> ? = 1
[1,2,4,3,-5] => [-1,-2,-4,-3,5] => [2,1]
=> [2,1]
=> 1
[1,2,4,-3,5] => [-1,-2,-4,3,-5] => []
=> []
=> ? = 1
[1,2,-4,3,5] => [-1,-2,4,-3,-5] => []
=> []
=> ? = 1
[1,2,-4,-3,5] => [-1,-2,4,3,-5] => [2]
=> [1,1]
=> ? = 1
[1,2,-4,-3,-5] => [-1,-2,4,3,5] => [2,1]
=> [2,1]
=> 1
[1,-2,4,3,5] => [-1,2,-4,-3,-5] => [2,1]
=> [2,1]
=> 1
[1,-2,-4,-3,5] => [-1,2,4,3,-5] => [2,1]
=> [2,1]
=> 1
[-1,2,4,3,5] => [1,-2,-4,-3,-5] => [2,1]
=> [2,1]
=> 1
[-1,2,-4,-3,5] => [1,-2,4,3,-5] => [2,1]
=> [2,1]
=> 1
[1,2,4,5,3] => [-1,-2,-4,-5,-3] => []
=> []
=> ? = 1
[1,2,4,-5,-3] => [-1,-2,-4,5,3] => []
=> []
=> ? = 1
[1,2,-4,5,-3] => [-1,-2,4,-5,3] => []
=> []
=> ? = 1
[1,2,-4,-5,3] => [-1,-2,4,5,-3] => []
=> []
=> ? = 1
[1,2,5,3,4] => [-1,-2,-5,-3,-4] => []
=> []
=> ? = 1
[1,2,5,-3,-4] => [-1,-2,-5,3,4] => []
=> []
=> ? = 1
[1,2,-5,3,-4] => [-1,-2,5,-3,4] => []
=> []
=> ? = 1
[1,2,-5,-3,4] => [-1,-2,5,3,-4] => []
=> []
=> ? = 1
[1,2,5,-4,3] => [-1,-2,-5,4,-3] => [2,1]
=> [2,1]
=> 1
[1,2,-5,-4,-3] => [-1,-2,5,4,3] => [2,1]
=> [2,1]
=> 1
[1,-2,5,4,3] => [-1,2,-5,-4,-3] => [2,1]
=> [2,1]
=> 1
[1,-2,-5,4,-3] => [-1,2,5,-4,3] => [2,1]
=> [2,1]
=> 1
[-1,2,5,4,3] => [1,-2,-5,-4,-3] => [2,1]
=> [2,1]
=> 1
[-1,2,-5,4,-3] => [1,-2,5,-4,3] => [2,1]
=> [2,1]
=> 1
[1,3,2,4,-5] => [-1,-3,-2,-4,5] => [2,1]
=> [2,1]
=> 1
[1,3,2,-4,5] => [-1,-3,-2,4,-5] => [2,1]
=> [2,1]
=> 1
[1,-3,-2,4,-5] => [-1,3,2,-4,5] => [2,1]
=> [2,1]
=> 1
[1,-3,-2,-4,5] => [-1,3,2,4,-5] => [2,1]
=> [2,1]
=> 1
[-1,3,2,4,5] => [1,-3,-2,-4,-5] => [2,1]
=> [2,1]
=> 1
[-1,-3,-2,4,5] => [1,3,2,-4,-5] => [2,1]
=> [2,1]
=> 1
[1,3,2,5,4] => [-1,-3,-2,-5,-4] => [2,2]
=> [2,2]
=> 2
[1,3,2,-5,-4] => [-1,-3,-2,5,4] => [2,2]
=> [2,2]
=> 2
[1,-3,-2,5,4] => [-1,3,2,-5,-4] => [2,2]
=> [2,2]
=> 2
[1,-3,-2,-5,-4] => [-1,3,2,5,4] => [2,2]
=> [2,2]
=> 2
[-1,3,2,5,4] => [1,-3,-2,-5,-4] => [2,2,1]
=> [3,2]
=> 2
[-1,3,2,-5,-4] => [1,-3,-2,5,4] => [2,2,1]
=> [3,2]
=> 2
[-1,-3,-2,5,4] => [1,3,2,-5,-4] => [2,2,1]
=> [3,2]
=> 2
[-1,-3,-2,-5,-4] => [1,3,2,5,4] => [2,2,1]
=> [3,2]
=> 2
[1,4,3,2,-5] => [-1,-4,-3,-2,5] => [2,1]
=> [2,1]
=> 1
[1,4,-3,2,5] => [-1,-4,3,-2,-5] => [2,1]
=> [2,1]
=> 1
[1,-4,3,-2,-5] => [-1,4,-3,2,5] => [2,1]
=> [2,1]
=> 1
[1,-4,-3,-2,5] => [-1,4,3,2,-5] => [2,1]
=> [2,1]
=> 1
[-1,4,3,2,5] => [1,-4,-3,-2,-5] => [2,1]
=> [2,1]
=> 1
[-1,-4,3,-2,5] => [1,4,-3,2,-5] => [2,1]
=> [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.
Matching statistic: St001816
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St001816: Standard tableaux ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 29%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St001816: Standard tableaux ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,3,4] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1
[1,2,3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,-3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,-2,3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,2,3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,2,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,3,2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[2,1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-2,-1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[2,1,4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[2,1,-4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-2,-1,4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-2,-1,-4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[3,2,1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-3,2,-1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[3,4,1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[3,-4,1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-3,4,-1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-3,-4,-1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[4,2,3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-4,2,3,-1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[4,3,2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[4,-3,-2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-4,3,2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-4,-3,-2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [[1,2,4,6,8],[3,5,7,9,10]]
=> ? = 1
[1,2,3,4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1
[1,2,3,-4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1
[1,2,3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,-3,4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1
[1,2,-3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,-3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,-2,3,4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1
[1,-2,3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,-2,3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,-2,-3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,2,3,4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1
[-1,2,3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,2,3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,2,-3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,-2,3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,3,5,4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1
[1,2,3,5,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,3,-5,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,3,-5,-4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1
[1,2,-3,5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,2,-3,-5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-2,3,5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-2,3,-5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-1,2,3,5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-1,2,3,-5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,2,4,3,5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1
[1,2,4,3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,2,4,-3,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,-4,3,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,-4,-3,5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1
[1,2,-4,-3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-2,4,3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-2,-4,-3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-1,2,4,3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-1,2,-4,-3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,2,4,5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,4,-5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,-4,5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,-4,-5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,5,3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,5,-3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,-5,3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,-5,-3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1
[1,2,5,4,3] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1
[1,2,5,4,-3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,5,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,2,-5,4,3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,2,-5,4,-3] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1
[1,2,-5,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-2,5,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,-2,-5,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[-1,2,5,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1
[1,3,-2,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,-3,2,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,3,2,5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,3,2,-5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,-3,-2,5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,-3,-2,-5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[1,4,3,-2,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,-4,3,2,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,4,5,2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,4,-5,2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,-4,5,-2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,-4,-5,-2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[1,5,3,4,-2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[1,-5,3,4,2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 1
[-1,5,4,3,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,5,-4,-3,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
[-1,-5,4,3,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 2
Description
Eigenvalues of the top-to-random operator acting on a simple module.
These eigenvalues are given in [1] and [3].
The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module.
This statistic bears different names, such as the type in [2] or eig in [3].
Similarly, the eigenvalues of the random-to-random operator acting on a simple module is [[St000508]].
Matching statistic: St000075
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000075: Standard tableaux ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 29%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000075: Standard tableaux ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 29%
Values
[1,2,3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,3,4] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1 + 1
[1,2,3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,-3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,-2,3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,2,3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,2,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,3,2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[2,1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-2,-1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[2,1,4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[2,1,-4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-2,-1,4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-2,-1,-4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[3,2,1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-3,2,-1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[3,4,1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[3,-4,1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-3,4,-1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-3,-4,-1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[4,2,3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-4,2,3,-1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[4,3,2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[4,-3,-2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-4,3,2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-4,-3,-2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [[1,2,4,6,8],[3,5,7,9,10]]
=> ? = 1 + 1
[1,2,3,4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1 + 1
[1,2,3,-4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1 + 1
[1,2,3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,-3,4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1 + 1
[1,2,-3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,-3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,-2,3,4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1 + 1
[1,-2,3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,-2,3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,-2,-3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,2,3,4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 1 + 1
[-1,2,3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,2,3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,2,-3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,-2,3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,3,5,4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1 + 1
[1,2,3,5,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,3,-5,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,3,-5,-4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1 + 1
[1,2,-3,5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,2,-3,-5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-2,3,5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-2,3,-5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-1,2,3,5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-1,2,3,-5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,2,4,3,5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1 + 1
[1,2,4,3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,2,4,-3,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,-4,3,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,-4,-3,5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1 + 1
[1,2,-4,-3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-2,4,3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-2,-4,-3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-1,2,4,3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-1,2,-4,-3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,2,4,5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,4,-5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,-4,5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,-4,-5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,5,3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,5,-3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,-5,3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,-5,-3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 1 + 1
[1,2,5,4,3] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1 + 1
[1,2,5,4,-3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,5,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,2,-5,4,3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,2,-5,4,-3] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 1 + 1
[1,2,-5,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-2,5,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,-2,-5,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[-1,2,5,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 1
[1,3,-2,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,-3,2,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,3,2,5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,3,2,-5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,-3,-2,5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,-3,-2,-5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[1,4,3,-2,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,-4,3,2,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,4,5,2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,4,-5,2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,-4,5,-2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,-4,-5,-2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[1,5,3,4,-2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[1,-5,3,4,2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 1 + 1
[-1,5,4,3,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,5,-4,-3,2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
[-1,-5,4,3,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [[1,2,3],[4,5,6]]
=> 3 = 2 + 1
Description
The orbit size of a standard tableau under promotion.
The following 11 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000933The number of multipartitions of sizes given by an integer partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St001713The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern. St001964The interval resolution global dimension of a poset. St000181The number of connected components of the Hasse diagram for the poset. St000635The number of strictly order preserving maps of a poset into itself. St001890The maximum magnitude of the Möbius function of a poset.
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