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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000590
(load all 57 compositions to match this statistic)
(load all 57 compositions to match this statistic)
St000590: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 0
{{1},{2}}
=> 0
{{1,2,3}}
=> 0
{{1,2},{3}}
=> 0
{{1,3},{2}}
=> 0
{{1},{2,3}}
=> 1
{{1},{2},{3}}
=> 0
{{1,2,3,4}}
=> 0
{{1,2,3},{4}}
=> 0
{{1,2,4},{3}}
=> 0
{{1,2},{3,4}}
=> 1
{{1,2},{3},{4}}
=> 0
{{1,3,4},{2}}
=> 0
{{1,3},{2,4}}
=> 0
{{1,3},{2},{4}}
=> 0
{{1,4},{2,3}}
=> 0
{{1},{2,3,4}}
=> 1
{{1},{2,3},{4}}
=> 1
{{1,4},{2},{3}}
=> 0
{{1},{2,4},{3}}
=> 1
{{1},{2},{3,4}}
=> 2
{{1},{2},{3},{4}}
=> 0
{{1,2,3,4,5}}
=> 0
{{1,2,3,4},{5}}
=> 0
{{1,2,3,5},{4}}
=> 0
{{1,2,3},{4,5}}
=> 1
{{1,2,3},{4},{5}}
=> 0
{{1,2,4,5},{3}}
=> 0
{{1,2,4},{3,5}}
=> 0
{{1,2,4},{3},{5}}
=> 0
{{1,2,5},{3,4}}
=> 0
{{1,2},{3,4,5}}
=> 1
{{1,2},{3,4},{5}}
=> 1
{{1,2,5},{3},{4}}
=> 0
{{1,2},{3,5},{4}}
=> 1
{{1,2},{3},{4,5}}
=> 2
{{1,2},{3},{4},{5}}
=> 0
{{1,3,4,5},{2}}
=> 0
{{1,3,4},{2,5}}
=> 0
{{1,3,4},{2},{5}}
=> 0
{{1,3,5},{2,4}}
=> 0
{{1,3},{2,4,5}}
=> 0
{{1,3},{2,4},{5}}
=> 0
{{1,3,5},{2},{4}}
=> 0
{{1,3},{2,5},{4}}
=> 0
{{1,3},{2},{4,5}}
=> 2
{{1,3},{2},{4},{5}}
=> 0
{{1,4,5},{2,3}}
=> 0
{{1,4},{2,3,5}}
=> 0
{{1,4},{2,3},{5}}
=> 0
Description
The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block.
Matching statistic: St001867
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001867: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001867: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
{{1,2}}
=> [2,1] => [2,1] => 0
{{1},{2}}
=> [1,2] => [1,2] => 0
{{1,2,3}}
=> [2,3,1] => [2,3,1] => 0
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
=> [3,2,1] => [3,2,1] => 0
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [2,3,1,4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [2,4,3,1] => 0
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [3,2,4,1] => 0
{{1,3},{2,4}}
=> [3,4,1,2] => [3,4,1,2] => 0
{{1,3},{2},{4}}
=> [3,2,1,4] => [3,2,1,4] => 0
{{1,4},{2,3}}
=> [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,3,4}}
=> [1,3,4,2] => [1,3,4,2] => 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
=> [4,2,3,1] => [4,2,3,1] => 0
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,4,3,2] => 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => 2
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [2,3,4,5,1] => ? = 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [2,3,4,1,5] => ? = 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [2,3,5,4,1] => ? = 0
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [2,3,1,5,4] => ? = 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [2,3,1,4,5] => ? = 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [2,4,3,5,1] => ? = 0
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [2,4,5,1,3] => ? = 0
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [2,4,3,1,5] => ? = 0
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [2,5,4,3,1] => ? = 0
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => ? = 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [2,5,3,4,1] => ? = 0
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => ? = 2
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => ? = 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [3,2,4,5,1] => ? = 0
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [3,5,4,1,2] => ? = 0
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [3,2,4,1,5] => ? = 0
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [3,4,5,2,1] => ? = 0
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [3,4,1,5,2] => ? = 0
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [3,4,1,2,5] => ? = 0
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [3,2,5,4,1] => ? = 0
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [3,5,1,4,2] => ? = 0
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [3,2,1,5,4] => ? = 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [4,3,2,5,1] => ? = 0
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 0
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [4,3,2,1,5] => ? = 0
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [5,3,4,2,1] => ? = 0
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => 1
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,3,4,2,5] => 1
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [5,3,2,4,1] => ? = 0
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,3,5,4,2] => 1
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,3,2,5,4] => 3
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [4,2,3,5,1] => ? = 0
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [4,5,3,1,2] => ? = 0
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 1
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [4,2,3,1,5] => ? = 0
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,4,3,5,2] => 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,4,5,2,3] => 2
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,4,3,2,5] => 1
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [5,2,4,3,1] => ? = 1
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [1,5,4,3,2] => 2
{{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,4,5,3] => 2
{{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [5,2,3,4,1] => ? = 0
{{1},{2,5},{3},{4}}
=> [1,5,3,4,2] => [1,5,3,4,2] => 1
{{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => [1,2,5,4,3] => 2
{{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => [1,2,3,5,4] => 3
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [2,3,4,5,6,1] => ? = 0
{{1,2,3,4,5},{6}}
=> [2,3,4,5,1,6] => [2,3,4,5,1,6] => ? = 0
{{1,2,3,4,6},{5}}
=> [2,3,4,6,5,1] => [2,3,4,6,5,1] => ? = 0
{{1,2,3,4},{5,6}}
=> [2,3,4,1,6,5] => [2,3,4,1,6,5] => ? = 1
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => [2,3,4,1,5,6] => ? = 0
{{1,2,3,5,6},{4}}
=> [2,3,5,4,6,1] => [2,3,5,4,6,1] => ? = 0
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => [2,3,5,6,1,4] => ? = 0
{{1,2,3,5},{4},{6}}
=> [2,3,5,4,1,6] => [2,3,5,4,1,6] => ? = 0
{{1,2,3,6},{4,5}}
=> [2,3,6,5,4,1] => [2,3,6,5,4,1] => ? = 0
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => [2,3,1,5,6,4] => ? = 1
{{1,2,3},{4,5},{6}}
=> [2,3,1,5,4,6] => [2,3,1,5,4,6] => ? = 1
{{1,2,3,6},{4},{5}}
=> [2,3,6,4,5,1] => [2,3,6,4,5,1] => ? = 0
{{1,2,3},{4,6},{5}}
=> [2,3,1,6,5,4] => [2,3,1,6,5,4] => ? = 1
Description
The number of alignments of type EN of a signed permutation.
An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold:
* $-i < 0 < -\pi(i) < \pi(j) < j$
* $i \leq\pi(i) < \pi(j) < j$.
Matching statistic: St001868
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00216: Set partitions —inverse Wachs-White⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001868: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 38%
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001868: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 38%
Values
{{1,2}}
=> {{1,2}}
=> [2,1] => [2,1] => 0
{{1},{2}}
=> {{1},{2}}
=> [1,2] => [1,2] => 0
{{1,2,3}}
=> {{1,2,3}}
=> [2,3,1] => [2,3,1] => 0
{{1,2},{3}}
=> {{1},{2,3}}
=> [1,3,2] => [1,3,2] => 0
{{1,3},{2}}
=> {{1,3},{2}}
=> [3,2,1] => [3,2,1] => 0
{{1},{2,3}}
=> {{1,2},{3}}
=> [2,1,3] => [2,1,3] => 1
{{1},{2},{3}}
=> {{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 0
{{1,2,3},{4}}
=> {{1},{2,3,4}}
=> [1,3,4,2] => [1,3,4,2] => 0
{{1,2,4},{3}}
=> {{1,3,4},{2}}
=> [3,2,4,1] => [3,2,4,1] => 0
{{1,2},{3,4}}
=> {{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}}
=> {{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => 0
{{1,3,4},{2}}
=> {{1,3},{2,4}}
=> [3,4,1,2] => [3,4,1,2] => 0
{{1,3},{2,4}}
=> {{1,2,4},{3}}
=> [2,4,3,1] => [2,4,3,1] => 0
{{1,3},{2},{4}}
=> {{1},{2,4},{3}}
=> [1,4,3,2] => [1,4,3,2] => 0
{{1,4},{2,3}}
=> {{1,4},{2,3}}
=> [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,3,4}}
=> {{1,2,3},{4}}
=> [2,3,1,4] => [2,3,1,4] => 1
{{1},{2,3},{4}}
=> {{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
=> {{1,4},{2},{3}}
=> [4,2,3,1] => [4,2,3,1] => 0
{{1},{2,4},{3}}
=> {{1,3},{2},{4}}
=> [3,2,1,4] => [3,2,1,4] => 1
{{1},{2},{3,4}}
=> {{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => 2
{{1},{2},{3},{4}}
=> {{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
=> {{1,2,3,4,5}}
=> [2,3,4,5,1] => [2,3,4,5,1] => ? = 0
{{1,2,3,4},{5}}
=> {{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => 0
{{1,2,3,5},{4}}
=> {{1,3,4,5},{2}}
=> [3,2,4,5,1] => [3,2,4,5,1] => ? = 0
{{1,2,3},{4,5}}
=> {{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 1
{{1,2,3},{4},{5}}
=> {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,4,5,3] => 0
{{1,2,4,5},{3}}
=> {{1,3},{2,4,5}}
=> [3,4,1,5,2] => [3,4,1,5,2] => ? = 0
{{1,2,4},{3,5}}
=> {{1,2,4,5},{3}}
=> [2,4,3,5,1] => [2,4,3,5,1] => ? = 0
{{1,2,4},{3},{5}}
=> {{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,4,3,5,2] => 0
{{1,2,5},{3,4}}
=> {{1,4,5},{2,3}}
=> [4,3,2,5,1] => [4,3,2,5,1] => ? = 0
{{1,2},{3,4,5}}
=> {{1,2,3},{4,5}}
=> [2,3,1,5,4] => [2,3,1,5,4] => ? = 1
{{1,2},{3,4},{5}}
=> {{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,3,2,5,4] => 1
{{1,2,5},{3},{4}}
=> {{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [4,2,3,5,1] => ? = 0
{{1,2},{3,5},{4}}
=> {{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
{{1,2},{3},{4,5}}
=> {{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => ? = 2
{{1,2},{3},{4},{5}}
=> {{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1,3,4,5},{2}}
=> {{1,3,5},{2,4}}
=> [3,4,5,2,1] => [3,4,5,2,1] => ? = 0
{{1,3,4},{2,5}}
=> {{1,2,4},{3,5}}
=> [2,4,5,1,3] => [2,4,5,1,3] => ? = 0
{{1,3,4},{2},{5}}
=> {{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,4,5,2,3] => 0
{{1,3,5},{2,4}}
=> {{1,4},{2,3,5}}
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 0
{{1,3},{2,4,5}}
=> {{1,2,3,5},{4}}
=> [2,3,5,4,1] => [2,3,5,4,1] => ? = 0
{{1,3},{2,4},{5}}
=> {{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,3,5,4,2] => 0
{{1,3,5},{2},{4}}
=> {{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 0
{{1,3},{2,5},{4}}
=> {{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [3,2,5,4,1] => ? = 0
{{1,3},{2},{4,5}}
=> {{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 2
{{1,3},{2},{4},{5}}
=> {{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => [1,2,5,4,3] => 0
{{1,4,5},{2,3}}
=> {{1,3,4},{2,5}}
=> [3,5,4,1,2] => [3,5,4,1,2] => ? = 0
{{1,4},{2,3,5}}
=> {{1,2,5},{3,4}}
=> [2,5,4,3,1] => [2,5,4,3,1] => ? = 0
{{1,4},{2,3},{5}}
=> {{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [1,5,4,3,2] => 0
{{1,5},{2,3,4}}
=> {{1,5},{2,3,4}}
=> [5,3,4,2,1] => [5,3,4,2,1] => ? = 0
{{1},{2,3,4,5}}
=> {{1,2,3,4},{5}}
=> [2,3,4,1,5] => [2,3,4,1,5] => ? = 1
{{1},{2,3,4},{5}}
=> {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,3,4,2,5] => 1
{{1,5},{2,3},{4}}
=> {{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [5,2,4,3,1] => ? = 0
{{1},{2,3,5},{4}}
=> {{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [3,2,4,1,5] => ? = 1
{{1},{2,3},{4,5}}
=> {{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => ? = 3
{{1},{2,3},{4},{5}}
=> {{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1,4,5},{2},{3}}
=> {{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [4,5,3,1,2] => ? = 0
{{1,4},{2,5},{3}}
=> {{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [3,5,1,4,2] => ? = 0
{{1,4},{2},{3,5}}
=> {{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [2,5,3,4,1] => ? = 1
{{1,4},{2},{3},{5}}
=> {{1},{2,5},{3},{4}}
=> [1,5,3,4,2] => [1,5,3,4,2] => 0
{{1,5},{2,4},{3}}
=> {{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
{{1},{2,4,5},{3}}
=> {{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [3,4,1,2,5] => ? = 1
{{1},{2,4},{3,5}}
=> {{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [2,4,3,1,5] => ? = 2
{{1},{2,4},{3},{5}}
=> {{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,4,3,2,5] => 1
{{1,5},{2},{3,4}}
=> {{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [5,3,2,4,1] => ? = 1
{{1},{2,5},{3,4}}
=> {{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [4,3,2,1,5] => ? = 2
{{1},{2},{3,4,5}}
=> {{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [2,3,1,4,5] => ? = 2
{{1},{2},{3,4},{5}}
=> {{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,5},{2},{3},{4}}
=> {{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [5,2,3,4,1] => ? = 0
{{1},{2,5},{3},{4}}
=> {{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [4,2,3,1,5] => ? = 1
{{1},{2},{3,5},{4}}
=> {{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [3,2,1,4,5] => ? = 2
{{1},{2},{3},{4,5}}
=> {{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => ? = 3
{{1},{2},{3},{4},{5}}
=> {{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4,5,6}}
=> {{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [2,3,4,5,6,1] => ? = 0
{{1,2,3,4,5},{6}}
=> {{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [1,3,4,5,6,2] => ? = 0
{{1,2,3,4,6},{5}}
=> {{1,3,4,5,6},{2}}
=> [3,2,4,5,6,1] => [3,2,4,5,6,1] => ? = 0
{{1,2,3,4},{5,6}}
=> {{1,2},{3,4,5,6}}
=> [2,1,4,5,6,3] => [2,1,4,5,6,3] => ? = 1
{{1,2,3,4},{5},{6}}
=> {{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,2,4,5,6,3] => ? = 0
{{1,2,3,5,6},{4}}
=> {{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => [3,4,1,5,6,2] => ? = 0
{{1,2,3,5},{4,6}}
=> {{1,2,4,5,6},{3}}
=> [2,4,3,5,6,1] => [2,4,3,5,6,1] => ? = 0
{{1,2,3,5},{4},{6}}
=> {{1},{2,4,5,6},{3}}
=> [1,4,3,5,6,2] => [1,4,3,5,6,2] => ? = 0
{{1,2,3,6},{4,5}}
=> {{1,4,5,6},{2,3}}
=> [4,3,2,5,6,1] => [4,3,2,5,6,1] => ? = 0
{{1,2,3},{4,5,6}}
=> {{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => [2,3,1,5,6,4] => ? = 1
{{1,2,3},{4,5},{6}}
=> {{1},{2,3},{4,5,6}}
=> [1,3,2,5,6,4] => [1,3,2,5,6,4] => ? = 1
{{1,2,3,6},{4},{5}}
=> {{1,4,5,6},{2},{3}}
=> [4,2,3,5,6,1] => [4,2,3,5,6,1] => ? = 0
{{1,2,3},{4,6},{5}}
=> {{1,3},{2},{4,5,6}}
=> [3,2,1,5,6,4] => [3,2,1,5,6,4] => ? = 1
Description
The number of alignments of type NE of a signed permutation.
An alignment of type NE of a signed permutation $\pi\in\mathfrak H_n$ is a pair $1 \leq i, j\leq n$ such that $\pi(i) < i < j \leq \pi(j)$.
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