Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001605
Mapping
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00190: Signed permutations —Foata-Han⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2,3] => [1,2,3] => [1,1,1]
 => 2
[2,3,1] => [3,2,1] => [-2,-3,1] => [3]
 => 1
[2,-3,1] => [-3,2,-1] => [2,-3,-1] => [3]
 => 1
[3,1,2] => [3,2,1] => [-2,-3,1] => [3]
 => 1
[-3,1,2] => [-3,2,-1] => [2,-3,-1] => [3]
 => 1
[3,2,1] => [3,2,1] => [-2,-3,1] => [3]
 => 1
[-3,2,1] => [-3,2,-1] => [2,-3,-1] => [3]
 => 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,1,1,1]
 => 6
[1,2,3,-4] => [1,2,3,-4] => [1,2,3,-4] => [1,1,1]
 => 2
[1,2,4,-3] => [1,2,-3,4] => [1,2,-3,4] => [1,1,1]
 => 2
[1,3,4,2] => [1,4,3,2] => [1,-3,-4,2] => [3,1]
 => 1
[1,3,4,-2] => [1,-2,3,4] => [1,-2,3,4] => [1,1,1]
 => 2
[1,3,-4,2] => [1,-4,3,-2] => [1,3,-4,-2] => [3,1]
 => 1
[1,4,2,3] => [1,4,3,2] => [1,-3,-4,2] => [3,1]
 => 1
[1,-4,2,3] => [1,-4,3,-2] => [1,3,-4,-2] => [3,1]
 => 1
[1,4,3,2] => [1,4,3,2] => [1,-3,-4,2] => [3,1]
 => 1
[1,-4,3,2] => [1,-4,3,-2] => [1,3,-4,-2] => [3,1]
 => 1
[2,3,1,4] => [3,2,1,4] => [-2,-3,1,4] => [3,1]
 => 1
[2,3,1,-4] => [3,2,1,-4] => [-2,-3,1,-4] => [3]
 => 1
[2,-3,1,4] => [-3,2,-1,4] => [2,-3,-1,4] => [3,1]
 => 1
[2,-3,1,-4] => [-3,2,-1,-4] => [2,-3,-1,-4] => [3]
 => 1
[2,3,4,-1] => [-1,2,3,4] => [-1,2,3,4] => [1,1,1]
 => 2
[2,-3,4,1] => [-3,2,-1,4] => [2,-3,-1,4] => [3,1]
 => 1
[2,-3,-4,1] => [-3,2,-1,-4] => [2,-3,-1,-4] => [3]
 => 1
[2,-4,1,-3] => [-4,2,-3,-1] => [-3,4,2,-1] => [4]
 => 1
[2,4,-3,1] => [-3,2,-1,4] => [2,-3,-1,4] => [3,1]
 => 1
[2,-4,-3,1] => [-3,2,-1,-4] => [2,-3,-1,-4] => [3]
 => 1
[3,1,2,4] => [3,2,1,4] => [-2,-3,1,4] => [3,1]
 => 1
[3,1,2,-4] => [3,2,1,-4] => [-2,-3,1,-4] => [3]
 => 1
[-3,1,2,4] => [-3,2,-1,4] => [2,-3,-1,4] => [3,1]
 => 1
[-3,1,2,-4] => [-3,2,-1,-4] => [2,-3,-1,-4] => [3]
 => 1
[3,1,4,2] => [3,4,1,2] => [3,4,1,2] => [2,2]
 => 2
[3,1,-4,2] => [3,-4,1,-2] => [3,-4,1,-2] => [2,2]
 => 2
[-3,1,4,2] => [-3,4,-1,2] => [-3,4,-1,2] => [2,2]
 => 2
[-3,1,-4,2] => [-3,-4,-1,-2] => [-3,-4,-1,-2] => [2,2]
 => 2
[3,2,1,4] => [3,2,1,4] => [-2,-3,1,4] => [3,1]
 => 1
[3,2,1,-4] => [3,2,1,-4] => [-2,-3,1,-4] => [3]
 => 1
[-3,2,1,4] => [-3,2,-1,4] => [2,-3,-1,4] => [3,1]
 => 1
[-3,2,1,-4] => [-3,2,-1,-4] => [2,-3,-1,-4] => [3]
 => 1
[-3,2,4,1] => [-3,4,-1,2] => [-3,4,-1,2] => [2,2]
 => 2
[-3,2,-4,1] => [-3,-4,-1,-2] => [-3,-4,-1,-2] => [2,2]
 => 2
[3,4,1,-2] => [4,-2,3,1] => [3,-4,-2,1] => [4]
 => 1
[-3,4,1,2] => [-3,4,-1,2] => [-3,4,-1,2] => [2,2]
 => 2
[-3,-4,1,2] => [-3,-4,-1,-2] => [-3,-4,-1,-2] => [2,2]
 => 2
[3,4,2,-1] => [-1,4,3,2] => [-1,-3,-4,2] => [3]
 => 1
[3,-4,2,-1] => [-1,-4,3,-2] => [-1,3,-4,-2] => [3]
 => 1
[-3,4,2,1] => [-3,4,-1,2] => [-3,4,-1,2] => [2,2]
 => 2
[-3,-4,2,1] => [-3,-4,-1,-2] => [-3,-4,-1,-2] => [2,2]
 => 2
[-4,1,2,-3] => [-4,2,-3,-1] => [-3,4,2,-1] => [4]
 => 1
[4,1,3,-2] => [4,-2,3,1] => [3,-4,-2,1] => [4]
 => 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.