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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001605
Mp00252: Permutations —restriction⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3,4,5] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,3,5,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,5,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,5,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[5,1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,3,4,5,6] => [1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 6
[1,2,3,4,6,5] => [1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 6
[1,2,3,5,4,6] => [1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,3,5,6,4] => [1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,3,6,4,5] => [1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 6
[1,2,3,6,5,4] => [1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,4,3,5,6] => [1,2,4,3,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,4,3,6,5] => [1,2,4,3,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,4,6,3,5] => [1,2,4,3,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,5,4,3,6] => [1,2,5,4,3] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,5,4,6,3] => [1,2,5,4,3] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,5,6,4,3] => [1,2,5,4,3] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,6,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 6
[1,2,6,3,5,4] => [1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,6,4,3,5] => [1,2,4,3,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,2,6,5,4,3] => [1,2,5,4,3] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,3,2,4,5,6] => [1,3,2,4,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,3,2,4,6,5] => [1,3,2,4,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,3,2,5,4,6] => [1,3,2,5,4] => [2,2,1]
=> [2,1]
=> 1
[1,3,2,5,6,4] => [1,3,2,5,4] => [2,2,1]
=> [2,1]
=> 1
[1,3,2,6,4,5] => [1,3,2,4,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,3,2,6,5,4] => [1,3,2,5,4] => [2,2,1]
=> [2,1]
=> 1
[1,3,6,2,4,5] => [1,3,2,4,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,3,6,2,5,4] => [1,3,2,5,4] => [2,2,1]
=> [2,1]
=> 1
[1,4,3,2,5,6] => [1,4,3,2,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,4,3,2,6,5] => [1,4,3,2,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,4,3,6,2,5] => [1,4,3,2,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,4,5,2,3,6] => [1,4,5,2,3] => [2,2,1]
=> [2,1]
=> 1
[1,4,5,2,6,3] => [1,4,5,2,3] => [2,2,1]
=> [2,1]
=> 1
[1,4,5,6,2,3] => [1,4,5,2,3] => [2,2,1]
=> [2,1]
=> 1
[1,4,6,3,2,5] => [1,4,3,2,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,4,6,5,2,3] => [1,4,5,2,3] => [2,2,1]
=> [2,1]
=> 1
[1,5,3,4,2,6] => [1,5,3,4,2] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,5,3,4,6,2] => [1,5,3,4,2] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,5,3,6,4,2] => [1,5,3,4,2] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,5,4,3,2,6] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,4,3,6,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,4,6,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,6,3,4,2] => [1,5,3,4,2] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,5,6,4,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,6,2,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 6
[1,6,2,3,5,4] => [1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,6,2,4,3,5] => [1,2,4,3,5] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,6,2,5,4,3] => [1,2,5,4,3] => [2,1,1,1]
=> [1,1,1]
=> 2
[1,6,3,2,4,5] => [1,3,2,4,5] => [2,1,1,1]
=> [1,1,1]
=> 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.
Matching statistic: St001769
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00252: Permutations —restriction⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001769: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 10%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001769: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 10%
Values
[1,2,3,4,5] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,2,3,5,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,2,5,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,5,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[5,1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,2,3,4,5,6] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,3,4,6,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,3,5,4,6] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,3,5,6,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,3,6,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,3,6,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,4,3,5,6] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,4,3,6,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,4,6,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,5,4,3,6] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,2,5,4,6,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,2,5,6,4,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,2,6,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,6,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,6,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,6,5,4,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,3,2,4,5,6] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,2,4,6,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,2,5,4,6] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,3,2,5,6,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,3,2,6,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,2,6,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,3,6,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,6,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,4,3,2,5,6] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,3,2,6,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,3,6,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,5,2,3,6] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,4,5,2,6,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,4,5,6,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,4,6,3,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,6,5,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,5,3,4,2,6] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,3,4,6,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,3,6,4,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,4,3,2,6] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,5,4,3,6,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,5,4,6,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,5,6,3,4,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,6,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,6,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,6,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,6,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,6,2,5,4,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,6,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,6,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,6,4,3,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,6,4,5,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,6,5,3,4,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,6,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[2,1,3,4,5,6] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,3,4,6,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,3,5,4,6] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,3,5,6,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,3,6,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,3,6,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,4,3,5,6] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,4,3,6,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,4,6,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,5,4,3,6] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,1,5,4,6,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,1,5,6,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,1,6,3,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,6,3,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,6,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,6,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,6,1,3,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,6,1,3,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,6,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,6,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[6,2,1,3,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[6,2,1,3,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[6,2,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[6,2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
Description
The reflection length of a signed permutation.
This is the minimal numbers of reflections needed to express a signed permutation.
Matching statistic: St001864
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00252: Permutations —restriction⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001864: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 10%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001864: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 10%
Values
[1,2,3,4,5] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,2,3,5,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,2,5,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,5,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[5,1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3 = 2 + 1
[1,2,3,4,5,6] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,3,4,6,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,3,5,4,6] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,3,5,6,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,3,6,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,3,6,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,4,3,5,6] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,4,3,6,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,4,6,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,5,4,3,6] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,2,5,4,6,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,2,5,6,4,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,2,6,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,2,6,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,2,6,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,2,6,5,4,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,3,2,4,5,6] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,2,4,6,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,2,5,4,6] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,3,2,5,6,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,3,2,6,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,2,6,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,3,6,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,3,6,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,4,3,2,5,6] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,3,2,6,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,3,6,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,5,2,3,6] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,4,5,2,6,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,4,5,6,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,4,6,3,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,4,6,5,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,5,3,4,2,6] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,3,4,6,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,3,6,4,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,4,3,2,6] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,5,4,3,6,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,5,4,6,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,5,6,3,4,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,5,6,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[1,6,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 6 + 1
[1,6,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 2 + 1
[1,6,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2 + 1
[1,6,2,5,4,3] => [1,2,5,4,3] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 2 + 1
[1,6,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2 + 1
[1,6,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,6,4,3,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => [4,3,2,5,1] => ? = 2 + 1
[1,6,4,5,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 1 + 1
[1,6,5,3,4,2] => [1,5,3,4,2] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 2 + 1
[1,6,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 1 + 1
[2,1,3,4,5,6] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,3,4,6,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,3,5,4,6] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,3,5,6,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,3,6,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,3,6,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,4,3,5,6] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,4,3,6,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,4,6,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,5,4,3,6] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,1,5,4,6,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,1,5,6,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,1,6,3,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,1,6,3,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,1,6,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,1,6,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[2,6,1,3,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[2,6,1,3,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[2,6,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[2,6,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
[6,2,1,3,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3 = 2 + 1
[6,2,1,3,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 2 = 1 + 1
[6,2,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 2 = 1 + 1
[6,2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 2 = 1 + 1
Description
The number of excedances of a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) > i\}\rvert$.
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