Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000959
Mapping
St000959: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 5
[1,2,3,4] => 1
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 5
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 6
[2,4,1,3] => 6
[2,4,3,1] => 18
[3,1,2,4] => 2
[3,1,4,2] => 6
[3,2,1,4] => 5
[3,2,4,1] => 18
[3,4,1,2] => 22
[3,4,2,1] => 62
[4,1,2,3] => 6
[4,1,3,2] => 18
[4,2,1,3] => 18
[4,2,3,1] => 73
[4,3,1,2] => 62
[4,3,2,1] => 210
[1,2,3,4,5] => 1
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 5
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 6
[1,3,5,2,4] => 6
[1,3,5,4,2] => 18
[1,4,2,3,5] => 2
[1,4,2,5,3] => 6
[1,4,3,2,5] => 5
[1,4,3,5,2] => 18
[1,4,5,2,3] => 22
Description
The number of strong Bruhat factorizations of a permutation. This is, the number of factorizations π=t1⋯tℓ for transpositions {ti∣1≤i≤ℓ} such that t1⋯ti has more inversions than t1⋯ti−1 for all 1≤i≤ℓ.