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Matching statistic: St001848
Mapping
St001848: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[-1] => 1
[1,2] => 0
[1,-2] => 1
[-1,2] => 6
[-1,-2] => 7
[2,1] => 1
[2,-1] => 3
[-2,1] => 4
[-2,-1] => 6
[1,2,3] => 0
[1,2,-3] => 1
[1,-2,3] => 6
[1,-2,-3] => 7
[-1,2,3] => 15
[-1,2,-3] => 16
[-1,-2,3] => 21
[-1,-2,-3] => 22
[1,3,2] => 1
[1,3,-2] => 3
[1,-3,2] => 4
[1,-3,-2] => 6
[-1,3,2] => 16
[-1,3,-2] => 18
[-1,-3,2] => 19
[-1,-3,-2] => 21
[2,1,3] => 1
[2,1,-3] => 2
[2,-1,3] => 10
[2,-1,-3] => 11
[-2,1,3] => 11
[-2,1,-3] => 12
[-2,-1,3] => 20
[-2,-1,-3] => 21
[2,3,1] => 3
[2,3,-1] => 6
[2,-3,1] => 6
[2,-3,-1] => 9
[-2,3,1] => 13
[-2,3,-1] => 16
[-2,-3,1] => 16
[-2,-3,-1] => 19
[3,1,2] => 3
[3,1,-2] => 5
[3,-1,2] => 12
[3,-1,-2] => 14
[-3,1,2] => 8
[-3,1,-2] => 10
[-3,-1,2] => 17
[-3,-1,-2] => 19
Description
The atomic length of a signed permutation. The atomic length of an element $w$ of a Weyl group is the sum of the heights of the inversions of $w$.