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Matching statistic: St001773
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Mapping
St001773: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[-1] => 0
[1,2] => 2
[1,-2] => 1
[-1,2] => 1
[-1,-2] => 0
[2,1] => 1
[2,-1] => 1
[-2,1] => 1
[-2,-1] => 1
[1,2,3] => 3
[1,2,-3] => 2
[1,-2,3] => 2
[1,-2,-3] => 1
[-1,2,3] => 2
[-1,2,-3] => 1
[-1,-2,3] => 1
[-1,-2,-3] => 0
[1,3,2] => 2
[1,3,-2] => 2
[1,-3,2] => 2
[1,-3,-2] => 2
[-1,3,2] => 1
[-1,3,-2] => 1
[-1,-3,2] => 1
[-1,-3,-2] => 1
[2,1,3] => 2
[2,1,-3] => 1
[2,-1,3] => 2
[2,-1,-3] => 1
[-2,1,3] => 2
[-2,1,-3] => 1
[-2,-1,3] => 2
[-2,-1,-3] => 1
[2,3,1] => 2
[2,3,-1] => 2
[2,-3,1] => 2
[2,-3,-1] => 2
[-2,3,1] => 2
[-2,3,-1] => 2
[-2,-3,1] => 1
[-2,-3,-1] => 1
[3,1,2] => 2
[3,1,-2] => 2
[3,-1,2] => 2
[3,-1,-2] => 1
[-3,1,2] => 2
[-3,1,-2] => 2
[-3,-1,2] => 2
[-3,-1,-2] => 1
Description
The number of minimal elements in Bruhat order not less than the signed permutation. The minimal elements in question are biGrassmannian, that is both the element and its inverse have at most one descent. This is the size of the essential set of the signed permutation, see [1].