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Matching statistic: St001819
Mapping
St001819: 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] => 1
[-1,-2] => 2
[2,1] => 2
[2,-1] => 3
[-2,1] => 3
[-2,-1] => 4
[1,2,3] => 0
[1,2,-3] => 1
[1,-2,3] => 1
[1,-2,-3] => 2
[-1,2,3] => 1
[-1,2,-3] => 2
[-1,-2,3] => 2
[-1,-2,-3] => 3
[1,3,2] => 4
[1,3,-2] => 5
[1,-3,2] => 5
[1,-3,-2] => 6
[-1,3,2] => 5
[-1,3,-2] => 6
[-1,-3,2] => 6
[-1,-3,-2] => 7
[2,1,3] => 2
[2,1,-3] => 3
[2,-1,3] => 3
[2,-1,-3] => 4
[-2,1,3] => 3
[-2,1,-3] => 4
[-2,-1,3] => 4
[-2,-1,-3] => 5
[2,3,1] => 6
[2,3,-1] => 7
[2,-3,1] => 7
[2,-3,-1] => 8
[-2,3,1] => 7
[-2,3,-1] => 8
[-2,-3,1] => 8
[-2,-3,-1] => 9
[3,1,2] => 2
[3,1,-2] => 3
[3,-1,2] => 3
[3,-1,-2] => 4
[-3,1,2] => 3
[-3,1,-2] => 4
[-3,-1,2] => 4
[-3,-1,-2] => 5
Description
The flag Denert index of a signed permutation. The flag Denert index of a signed permutation $\sigma$ is: $$fden(\sigma) = \operatorname{neg}(\sigma) + 2 \cdot den_B(\sigma),$$ where $den_B(\sigma) = den(perm(\sigma))$ is the Denert index of the associated permutation to $\sigma$.