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Your data matches 6 different statistics following compositions of up to 3 maps.
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Matching statistic: St001392
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001392: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001392: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1]
=> [1]
=> 0
[1,2] => [1,2] => [1,1]
=> [2]
=> 1
[1,-2] => [1,-2] => [1]
=> [1]
=> 0
[2,1] => [2,1] => [2]
=> [1,1]
=> 0
[2,-1] => [-1,2] => [1]
=> [1]
=> 0
[-2,1] => [-2,-1] => [2]
=> [1,1]
=> 0
[1,2,3] => [1,2,3] => [1,1,1]
=> [3]
=> 2
[1,2,-3] => [1,2,-3] => [1,1]
=> [2]
=> 1
[1,-2,3] => [1,-2,-3] => [1]
=> [1]
=> 0
[1,-2,-3] => [1,-2,-3] => [1]
=> [1]
=> 0
[-1,2,3] => [-1,-2,3] => [1]
=> [1]
=> 0
[1,3,2] => [1,3,2] => [2,1]
=> [2,1]
=> 0
[1,3,-2] => [1,-2,3] => [1,1]
=> [2]
=> 1
[1,-3,2] => [1,-3,-2] => [2,1]
=> [2,1]
=> 0
[1,-3,-2] => [1,-2,-3] => [1]
=> [1]
=> 0
[-1,3,2] => [-1,-2,3] => [1]
=> [1]
=> 0
[2,1,3] => [2,1,3] => [2,1]
=> [2,1]
=> 0
[2,1,-3] => [2,1,-3] => [2]
=> [1,1]
=> 0
[2,-1,3] => [-1,2,-3] => [1]
=> [1]
=> 0
[2,-1,-3] => [-1,2,-3] => [1]
=> [1]
=> 0
[-2,1,3] => [-2,-1,3] => [2,1]
=> [2,1]
=> 0
[-2,1,-3] => [-2,-1,-3] => [2]
=> [1,1]
=> 0
[2,3,1] => [3,2,1] => [2,1]
=> [2,1]
=> 0
[2,3,-1] => [-1,2,3] => [1,1]
=> [2]
=> 1
[2,-3,1] => [-3,2,-1] => [2,1]
=> [2,1]
=> 0
[2,-3,-1] => [-1,2,-3] => [1]
=> [1]
=> 0
[-2,3,1] => [-2,-1,3] => [2,1]
=> [2,1]
=> 0
[-2,-3,1] => [-2,-1,-3] => [2]
=> [1,1]
=> 0
[3,1,2] => [3,2,1] => [2,1]
=> [2,1]
=> 0
[3,1,-2] => [3,-2,1] => [2]
=> [1,1]
=> 0
[3,-1,2] => [-1,-2,3] => [1]
=> [1]
=> 0
[3,-1,-2] => [-1,-2,3] => [1]
=> [1]
=> 0
[-3,1,2] => [-3,2,-1] => [2,1]
=> [2,1]
=> 0
[-3,1,-2] => [-3,-2,-1] => [2]
=> [1,1]
=> 0
[3,2,1] => [3,2,1] => [2,1]
=> [2,1]
=> 0
[3,2,-1] => [-1,3,2] => [2]
=> [1,1]
=> 0
[3,-2,1] => [-2,-1,3] => [2,1]
=> [2,1]
=> 0
[3,-2,-1] => [-1,-2,3] => [1]
=> [1]
=> 0
[-3,2,1] => [-3,2,-1] => [2,1]
=> [2,1]
=> 0
[-3,2,-1] => [-1,-3,-2] => [2]
=> [1,1]
=> 0
[-3,-2,1] => [-2,-1,-3] => [2]
=> [1,1]
=> 0
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [4]
=> 3
[1,2,3,-4] => [1,2,3,-4] => [1,1,1]
=> [3]
=> 2
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [2]
=> 1
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [2]
=> 1
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [2]
=> 1
[1,-2,3,-4] => [1,-2,-3,-4] => [1]
=> [1]
=> 0
[1,-2,-3,4] => [1,-2,-3,-4] => [1]
=> [1]
=> 0
[1,-2,-3,-4] => [1,-2,-3,-4] => [1]
=> [1]
=> 0
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [2]
=> 1
Description
The largest nonnegative integer which is not a part and is smaller than the largest part of the partition.
Matching statistic: St001232
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 53% ●values known / values provided: 53%●distinct values known / distinct values provided: 100%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 53% ●values known / values provided: 53%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,2] => [1,2] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-2] => [1,-2] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[2,1] => [2,1] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[2,-1] => [-1,2] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-2,1] => [-2,-1] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[1,2,3] => [1,2,3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,2,-3] => [1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-2,3] => [1,-2,-3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,-2,-3] => [1,-2,-3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-1,2,3] => [-1,-2,3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,3,2] => [1,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,3,-2] => [1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-3,2] => [1,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,-3,-2] => [1,-2,-3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-1,3,2] => [-1,-2,3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[2,1,3] => [2,1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,1,-3] => [2,1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[2,-1,3] => [-1,2,-3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[2,-1,-3] => [-1,2,-3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-2,1,3] => [-2,-1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[-2,1,-3] => [-2,-1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[2,3,1] => [3,2,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,3,-1] => [-1,2,3] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[2,-3,1] => [-3,2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,-3,-1] => [-1,2,-3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-2,3,1] => [-2,-1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[-2,-3,1] => [-2,-1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[3,1,2] => [3,2,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[3,1,-2] => [3,-2,1] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[3,-1,2] => [-1,-2,3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[3,-1,-2] => [-1,-2,3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-3,1,2] => [-3,2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[-3,1,-2] => [-3,-2,-1] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[3,2,1] => [3,2,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[3,2,-1] => [-1,3,2] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[3,-2,1] => [-2,-1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[3,-2,-1] => [-1,-2,3] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-3,2,1] => [-3,2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[-3,2,-1] => [-1,-3,-2] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[-3,-2,1] => [-2,-1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4 = 3 + 1
[1,2,3,-4] => [1,2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-2,3,-4] => [1,-2,-3,-4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,-2,-3,4] => [1,-2,-3,-4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,-2,-3,-4] => [1,-2,-3,-4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[-1,2,3,-4] => [-1,-2,3,-4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,2,4,-3] => [1,2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,2,-4,3] => [1,2,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,2,-4,-3] => [1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-2,4,3] => [1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-2,4,-3] => [1,-2,-3,-4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,-2,-4,3] => [1,-2,-3,-4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,-2,-4,-3] => [1,-2,-3,-4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-1,2,4,3] => [-1,-2,4,3] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[-1,2,4,-3] => [-1,-2,-3,4] => [1]
=> [1,0,1,0]
=> 1 = 0 + 1
[-1,2,-4,3] => [-1,-2,-4,-3] => [2]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[1,3,2,4] => [1,3,2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,3,2,-4] => [1,3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,3,-2,4] => [1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,3,-2,-4] => [1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2 = 1 + 1
[1,-3,2,4] => [1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,-3,2,-4] => [1,-3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,3,-4,2] => [1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,-3,4,2] => [1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,-3,-4,2] => [1,-3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,4,2,-3] => [1,4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,-4,2,3] => [1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,-4,2,-3] => [1,-4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,4,3,-2] => [1,-2,4,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,4,-3,2] => [1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,-4,3,2] => [1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[1,-4,3,-2] => [1,-2,-4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[1,-4,-3,2] => [1,-3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,1,3,4] => [2,1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[2,1,3,-4] => [2,1,3,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[-2,1,3,4] => [-2,-1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[-2,1,3,-4] => [-2,-1,3,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,1,4,-3] => [2,1,-3,4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[-2,1,4,-3] => [-2,-1,-3,4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,3,1,4] => [3,2,1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[2,3,1,-4] => [3,2,1,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,-3,1,4] => [-3,2,-1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[2,-3,1,-4] => [-3,2,-1,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[-2,3,1,4] => [-2,-1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[-2,3,1,-4] => [-2,-1,3,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,3,4,1] => [4,2,3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[2,3,-4,1] => [-4,2,3,-1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[2,-3,4,1] => [-3,2,-1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[2,-3,-4,1] => [-3,2,-1,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
[2,4,1,3] => [4,2,3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 2 + 1
[2,4,1,-3] => [4,2,-3,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 0 + 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000993
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 80%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 80%
Values
[1] => [1] => [1]
=> []
=> ? = 0
[1,2] => [1,2] => [1,1]
=> [1]
=> ? = 1
[1,-2] => [1,-2] => [1]
=> []
=> ? = 0
[2,1] => [2,1] => [2]
=> []
=> ? = 0
[2,-1] => [-1,2] => [1]
=> []
=> ? = 0
[-2,1] => [-2,-1] => [2]
=> []
=> ? = 0
[1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,2,-3] => [1,2,-3] => [1,1]
=> [1]
=> ? = 1
[1,-2,3] => [1,-2,-3] => [1]
=> []
=> ? = 0
[1,-2,-3] => [1,-2,-3] => [1]
=> []
=> ? = 0
[-1,2,3] => [-1,-2,3] => [1]
=> []
=> ? = 0
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? = 0
[1,3,-2] => [1,-2,3] => [1,1]
=> [1]
=> ? = 1
[1,-3,2] => [1,-3,-2] => [2,1]
=> [1]
=> ? = 0
[1,-3,-2] => [1,-2,-3] => [1]
=> []
=> ? = 0
[-1,3,2] => [-1,-2,3] => [1]
=> []
=> ? = 0
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? = 0
[2,1,-3] => [2,1,-3] => [2]
=> []
=> ? = 0
[2,-1,3] => [-1,2,-3] => [1]
=> []
=> ? = 0
[2,-1,-3] => [-1,2,-3] => [1]
=> []
=> ? = 0
[-2,1,3] => [-2,-1,3] => [2,1]
=> [1]
=> ? = 0
[-2,1,-3] => [-2,-1,-3] => [2]
=> []
=> ? = 0
[2,3,1] => [3,2,1] => [2,1]
=> [1]
=> ? = 0
[2,3,-1] => [-1,2,3] => [1,1]
=> [1]
=> ? = 1
[2,-3,1] => [-3,2,-1] => [2,1]
=> [1]
=> ? = 0
[2,-3,-1] => [-1,2,-3] => [1]
=> []
=> ? = 0
[-2,3,1] => [-2,-1,3] => [2,1]
=> [1]
=> ? = 0
[-2,-3,1] => [-2,-1,-3] => [2]
=> []
=> ? = 0
[3,1,2] => [3,2,1] => [2,1]
=> [1]
=> ? = 0
[3,1,-2] => [3,-2,1] => [2]
=> []
=> ? = 0
[3,-1,2] => [-1,-2,3] => [1]
=> []
=> ? = 0
[3,-1,-2] => [-1,-2,3] => [1]
=> []
=> ? = 0
[-3,1,2] => [-3,2,-1] => [2,1]
=> [1]
=> ? = 0
[-3,1,-2] => [-3,-2,-1] => [2]
=> []
=> ? = 0
[3,2,1] => [3,2,1] => [2,1]
=> [1]
=> ? = 0
[3,2,-1] => [-1,3,2] => [2]
=> []
=> ? = 0
[3,-2,1] => [-2,-1,3] => [2,1]
=> [1]
=> ? = 0
[3,-2,-1] => [-1,-2,3] => [1]
=> []
=> ? = 0
[-3,2,1] => [-3,2,-1] => [2,1]
=> [1]
=> ? = 0
[-3,2,-1] => [-1,-3,-2] => [2]
=> []
=> ? = 0
[-3,-2,1] => [-2,-1,-3] => [2]
=> []
=> ? = 0
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,2,3,-4] => [1,2,3,-4] => [1,1,1]
=> [1,1]
=> 2
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [1]
=> ? = 1
[1,-2,3,-4] => [1,-2,-3,-4] => [1]
=> []
=> ? = 0
[1,-2,-3,4] => [1,-2,-3,-4] => [1]
=> []
=> ? = 0
[1,-2,-3,-4] => [1,-2,-3,-4] => [1]
=> []
=> ? = 0
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [1]
=> ? = 1
[-1,2,3,-4] => [-1,-2,3,-4] => [1]
=> []
=> ? = 0
[1,2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,2,4,-3] => [1,2,-3,4] => [1,1,1]
=> [1,1]
=> 2
[1,2,-4,3] => [1,2,-4,-3] => [2,1,1]
=> [1,1]
=> 2
[1,2,-4,-3] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1
[1,-2,4,3] => [1,-2,-3,4] => [1,1]
=> [1]
=> ? = 1
[1,3,2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,-3,2,4] => [1,-3,-2,4] => [2,1,1]
=> [1,1]
=> 2
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 2
[1,3,4,-2] => [1,-2,3,4] => [1,1,1]
=> [1,1]
=> 2
[1,3,-4,2] => [1,-4,3,-2] => [2,1,1]
=> [1,1]
=> 2
[1,-3,4,2] => [1,-3,-2,4] => [2,1,1]
=> [1,1]
=> 2
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 2
[1,-4,2,3] => [1,-4,3,-2] => [2,1,1]
=> [1,1]
=> 2
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 2
[1,4,-3,2] => [1,-3,-2,4] => [2,1,1]
=> [1,1]
=> 2
[1,-4,3,2] => [1,-4,3,-2] => [2,1,1]
=> [1,1]
=> 2
[2,1,3,4] => [2,1,3,4] => [2,1,1]
=> [1,1]
=> 2
[-2,1,3,4] => [-2,-1,3,4] => [2,1,1]
=> [1,1]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 1
[2,1,-4,3] => [2,1,-4,-3] => [2,2]
=> [2]
=> 1
[-2,1,4,3] => [-2,-1,4,3] => [2,2]
=> [2]
=> 1
[-2,1,-4,3] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> 1
[2,3,1,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 2
[2,-3,1,4] => [-3,2,-1,4] => [2,1,1]
=> [1,1]
=> 2
[-2,3,1,4] => [-2,-1,3,4] => [2,1,1]
=> [1,1]
=> 2
[2,3,4,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 2
[2,3,4,-1] => [-1,2,3,4] => [1,1,1]
=> [1,1]
=> 2
[2,3,-4,1] => [-4,2,3,-1] => [2,1,1]
=> [1,1]
=> 2
[2,-3,4,1] => [-3,2,-1,4] => [2,1,1]
=> [1,1]
=> 2
[-2,3,4,1] => [-2,-1,4,3] => [2,2]
=> [2]
=> 1
[-2,3,-4,1] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> 1
[2,4,1,3] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 2
[2,-4,1,3] => [-4,2,3,-1] => [2,1,1]
=> [1,1]
=> 2
[-2,4,1,3] => [-2,-1,4,3] => [2,2]
=> [2]
=> 1
[-2,-4,1,3] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> 1
[2,4,3,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 2
[2,4,-3,1] => [-3,2,-1,4] => [2,1,1]
=> [1,1]
=> 2
[2,-4,3,1] => [-4,2,3,-1] => [2,1,1]
=> [1,1]
=> 2
[-2,4,3,1] => [-2,-1,4,3] => [2,2]
=> [2]
=> 1
[-2,-4,3,1] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> 1
[3,1,2,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 2
[-3,1,2,4] => [-3,2,-1,4] => [2,1,1]
=> [1,1]
=> 2
[3,1,4,2] => [3,4,1,2] => [2,2]
=> [2]
=> 1
[3,1,-4,2] => [3,-4,1,-2] => [2,2]
=> [2]
=> 1
[-3,1,4,2] => [-3,4,-1,2] => [2,2]
=> [2]
=> 1
[-3,1,-4,2] => [-3,-4,-1,-2] => [2,2]
=> [2]
=> 1
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 2
[3,-2,1,4] => [-2,-1,3,4] => [2,1,1]
=> [1,1]
=> 2
[-3,2,1,4] => [-3,2,-1,4] => [2,1,1]
=> [1,1]
=> 2
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St001604
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 20%
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 20%
Values
[1] => [1] => []
=> ?
=> ? = 0
[1,2] => [1,2] => []
=> ?
=> ? = 1
[1,-2] => [1,-2] => [1]
=> []
=> ? = 0
[2,1] => [2,1] => []
=> ?
=> ? = 0
[2,-1] => [-1,2] => [1]
=> []
=> ? = 0
[-2,1] => [-2,-1] => []
=> ?
=> ? = 0
[1,2,3] => [1,2,3] => []
=> ?
=> ? = 2
[1,2,-3] => [1,2,-3] => [1]
=> []
=> ? = 1
[1,-2,3] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0
[1,-2,-3] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0
[-1,2,3] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0
[1,3,2] => [1,3,2] => []
=> ?
=> ? = 0
[1,3,-2] => [1,-2,3] => [1]
=> []
=> ? = 1
[1,-3,2] => [1,-3,-2] => []
=> ?
=> ? = 0
[1,-3,-2] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0
[-1,3,2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0
[2,1,3] => [2,1,3] => []
=> ?
=> ? = 0
[2,1,-3] => [2,1,-3] => [1]
=> []
=> ? = 0
[2,-1,3] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0
[2,-1,-3] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0
[-2,1,3] => [-2,-1,3] => []
=> ?
=> ? = 0
[-2,1,-3] => [-2,-1,-3] => [1]
=> []
=> ? = 0
[2,3,1] => [3,2,1] => []
=> ?
=> ? = 0
[2,3,-1] => [-1,2,3] => [1]
=> []
=> ? = 1
[2,-3,1] => [-3,2,-1] => []
=> ?
=> ? = 0
[2,-3,-1] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0
[-2,3,1] => [-2,-1,3] => []
=> ?
=> ? = 0
[-2,-3,1] => [-2,-1,-3] => [1]
=> []
=> ? = 0
[3,1,2] => [3,2,1] => []
=> ?
=> ? = 0
[3,1,-2] => [3,-2,1] => [1]
=> []
=> ? = 0
[3,-1,2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0
[3,-1,-2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0
[-3,1,2] => [-3,2,-1] => []
=> ?
=> ? = 0
[-3,1,-2] => [-3,-2,-1] => [1]
=> []
=> ? = 0
[3,2,1] => [3,2,1] => []
=> ?
=> ? = 0
[3,2,-1] => [-1,3,2] => [1]
=> []
=> ? = 0
[3,-2,1] => [-2,-1,3] => []
=> ?
=> ? = 0
[3,-2,-1] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0
[-3,2,1] => [-3,2,-1] => []
=> ?
=> ? = 0
[-3,2,-1] => [-1,-3,-2] => [1]
=> []
=> ? = 0
[-3,-2,1] => [-2,-1,-3] => [1]
=> []
=> ? = 0
[1,2,3,4] => [1,2,3,4] => []
=> ?
=> ? = 3
[1,2,3,-4] => [1,2,3,-4] => [1]
=> []
=> ? = 2
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [1]
=> ? = 1
[1,-2,3,-4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0
[1,-2,-3,4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0
[1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [1]
=> ? = 1
[1,-2,3,-4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,3,-4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,-4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,-4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,3,-4,5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,3,-4,-5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,-3,4,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,3,4,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,3,-5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,5,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,-5,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,-5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,3,-5,-4] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,-3,5,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,3,5,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,4,-3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,4,-3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,-3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,-3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,4,-3,5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,4,-3,-5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,4,3,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,4,-5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,5,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,-5,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-4,-5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,4,-5,-3] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,4,5,3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,5,-3,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,5,-3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-5,3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-5,-3,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-5,-3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,5,-3,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,5,-3,-4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,5,3,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,5,-4,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,5,-4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-5,4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-5,-4,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-5,-4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,5,-4,-3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,5,4,3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-3,-2,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001603
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 20%
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 20%
Values
[1] => [1] => []
=> ?
=> ? = 0 + 1
[1,2] => [1,2] => []
=> ?
=> ? = 1 + 1
[1,-2] => [1,-2] => [1]
=> []
=> ? = 0 + 1
[2,1] => [2,1] => []
=> ?
=> ? = 0 + 1
[2,-1] => [-1,2] => [1]
=> []
=> ? = 0 + 1
[-2,1] => [-2,-1] => []
=> ?
=> ? = 0 + 1
[1,2,3] => [1,2,3] => []
=> ?
=> ? = 2 + 1
[1,2,-3] => [1,2,-3] => [1]
=> []
=> ? = 1 + 1
[1,-2,3] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0 + 1
[1,-2,-3] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0 + 1
[-1,2,3] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 1
[1,3,2] => [1,3,2] => []
=> ?
=> ? = 0 + 1
[1,3,-2] => [1,-2,3] => [1]
=> []
=> ? = 1 + 1
[1,-3,2] => [1,-3,-2] => []
=> ?
=> ? = 0 + 1
[1,-3,-2] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0 + 1
[-1,3,2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 1
[2,1,3] => [2,1,3] => []
=> ?
=> ? = 0 + 1
[2,1,-3] => [2,1,-3] => [1]
=> []
=> ? = 0 + 1
[2,-1,3] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0 + 1
[2,-1,-3] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0 + 1
[-2,1,3] => [-2,-1,3] => []
=> ?
=> ? = 0 + 1
[-2,1,-3] => [-2,-1,-3] => [1]
=> []
=> ? = 0 + 1
[2,3,1] => [3,2,1] => []
=> ?
=> ? = 0 + 1
[2,3,-1] => [-1,2,3] => [1]
=> []
=> ? = 1 + 1
[2,-3,1] => [-3,2,-1] => []
=> ?
=> ? = 0 + 1
[2,-3,-1] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0 + 1
[-2,3,1] => [-2,-1,3] => []
=> ?
=> ? = 0 + 1
[-2,-3,1] => [-2,-1,-3] => [1]
=> []
=> ? = 0 + 1
[3,1,2] => [3,2,1] => []
=> ?
=> ? = 0 + 1
[3,1,-2] => [3,-2,1] => [1]
=> []
=> ? = 0 + 1
[3,-1,2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 1
[3,-1,-2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 1
[-3,1,2] => [-3,2,-1] => []
=> ?
=> ? = 0 + 1
[-3,1,-2] => [-3,-2,-1] => [1]
=> []
=> ? = 0 + 1
[3,2,1] => [3,2,1] => []
=> ?
=> ? = 0 + 1
[3,2,-1] => [-1,3,2] => [1]
=> []
=> ? = 0 + 1
[3,-2,1] => [-2,-1,3] => []
=> ?
=> ? = 0 + 1
[3,-2,-1] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 1
[-3,2,1] => [-3,2,-1] => []
=> ?
=> ? = 0 + 1
[-3,2,-1] => [-1,-3,-2] => [1]
=> []
=> ? = 0 + 1
[-3,-2,1] => [-2,-1,-3] => [1]
=> []
=> ? = 0 + 1
[1,2,3,4] => [1,2,3,4] => []
=> ?
=> ? = 3 + 1
[1,2,3,-4] => [1,2,3,-4] => [1]
=> []
=> ? = 2 + 1
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1 + 1
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1 + 1
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [1]
=> ? = 1 + 1
[1,-2,3,-4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0 + 1
[1,-2,-3,4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0 + 1
[1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0 + 1
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [1]
=> ? = 1 + 1
[1,-2,3,-4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,3,-4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,-4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,-4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,3,-4,5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,3,-4,-5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,-3,4,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,-2,3,4,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,3,-5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,5,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,-5,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-3,-5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,3,-5,-4] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,-3,5,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,-2,3,5,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,4,-3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,4,-3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,-3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,-3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,4,-3,5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,4,-3,-5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,-2,4,3,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,4,-5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,5,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,-5,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-4,-5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,4,-5,-3] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,-2,4,5,3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,5,-3,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,5,-3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-5,3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-5,-3,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-5,-3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,5,-3,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,5,-3,-4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,-2,5,3,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,5,-4,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,5,-4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-5,4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-5,-4,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-2,-5,-4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,2,5,-4,-3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[-1,-2,5,4,3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[1,-3,-2,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001605
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 20%
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 20%
Values
[1] => [1] => []
=> ?
=> ? = 0 + 2
[1,2] => [1,2] => []
=> ?
=> ? = 1 + 2
[1,-2] => [1,-2] => [1]
=> []
=> ? = 0 + 2
[2,1] => [2,1] => []
=> ?
=> ? = 0 + 2
[2,-1] => [-1,2] => [1]
=> []
=> ? = 0 + 2
[-2,1] => [-2,-1] => []
=> ?
=> ? = 0 + 2
[1,2,3] => [1,2,3] => []
=> ?
=> ? = 2 + 2
[1,2,-3] => [1,2,-3] => [1]
=> []
=> ? = 1 + 2
[1,-2,3] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0 + 2
[1,-2,-3] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0 + 2
[-1,2,3] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 2
[1,3,2] => [1,3,2] => []
=> ?
=> ? = 0 + 2
[1,3,-2] => [1,-2,3] => [1]
=> []
=> ? = 1 + 2
[1,-3,2] => [1,-3,-2] => []
=> ?
=> ? = 0 + 2
[1,-3,-2] => [1,-2,-3] => [1,1]
=> [1]
=> ? = 0 + 2
[-1,3,2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 2
[2,1,3] => [2,1,3] => []
=> ?
=> ? = 0 + 2
[2,1,-3] => [2,1,-3] => [1]
=> []
=> ? = 0 + 2
[2,-1,3] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0 + 2
[2,-1,-3] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0 + 2
[-2,1,3] => [-2,-1,3] => []
=> ?
=> ? = 0 + 2
[-2,1,-3] => [-2,-1,-3] => [1]
=> []
=> ? = 0 + 2
[2,3,1] => [3,2,1] => []
=> ?
=> ? = 0 + 2
[2,3,-1] => [-1,2,3] => [1]
=> []
=> ? = 1 + 2
[2,-3,1] => [-3,2,-1] => []
=> ?
=> ? = 0 + 2
[2,-3,-1] => [-1,2,-3] => [1,1]
=> [1]
=> ? = 0 + 2
[-2,3,1] => [-2,-1,3] => []
=> ?
=> ? = 0 + 2
[-2,-3,1] => [-2,-1,-3] => [1]
=> []
=> ? = 0 + 2
[3,1,2] => [3,2,1] => []
=> ?
=> ? = 0 + 2
[3,1,-2] => [3,-2,1] => [1]
=> []
=> ? = 0 + 2
[3,-1,2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 2
[3,-1,-2] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 2
[-3,1,2] => [-3,2,-1] => []
=> ?
=> ? = 0 + 2
[-3,1,-2] => [-3,-2,-1] => [1]
=> []
=> ? = 0 + 2
[3,2,1] => [3,2,1] => []
=> ?
=> ? = 0 + 2
[3,2,-1] => [-1,3,2] => [1]
=> []
=> ? = 0 + 2
[3,-2,1] => [-2,-1,3] => []
=> ?
=> ? = 0 + 2
[3,-2,-1] => [-1,-2,3] => [1,1]
=> [1]
=> ? = 0 + 2
[-3,2,1] => [-3,2,-1] => []
=> ?
=> ? = 0 + 2
[-3,2,-1] => [-1,-3,-2] => [1]
=> []
=> ? = 0 + 2
[-3,-2,1] => [-2,-1,-3] => [1]
=> []
=> ? = 0 + 2
[1,2,3,4] => [1,2,3,4] => []
=> ?
=> ? = 3 + 2
[1,2,3,-4] => [1,2,3,-4] => [1]
=> []
=> ? = 2 + 2
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1 + 2
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [1]
=> ? = 1 + 2
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [1]
=> ? = 1 + 2
[1,-2,3,-4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0 + 2
[1,-2,-3,4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0 + 2
[1,-2,-3,-4] => [1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> ? = 0 + 2
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [1]
=> ? = 1 + 2
[1,-2,3,-4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,3,-4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,-4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,-4,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,3,-4,5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,3,-4,-5] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,-3,4,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,-2,3,4,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,3,-5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,5,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,-5,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-3,-5,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,3,-5,-4] => [-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,-3,5,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,-2,3,5,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,4,-3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,4,-3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,-3,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,-3,-5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,4,-3,5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,4,-3,-5] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,-2,4,3,5] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,4,-5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,5,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,-5,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-4,-5,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,4,-5,-3] => [-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,-2,4,5,3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,5,-3,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,5,-3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-5,3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-5,-3,4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-5,-3,-4] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,5,-3,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,5,-3,-4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,-2,5,3,4] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,5,-4,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,5,-4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-5,4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-5,-4,3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-2,-5,-4,-3] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,2,5,-4,-3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[-1,-2,5,4,3] => [-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
[1,-3,-2,4,5] => [1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> 2 = 0 + 2
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.
Sorry, this statistic was not found in the database
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