FlagDenertIndex on SignedPermutation

The negative entries plus twice the Denert index of the permutation |p(1)| ... |p(n)|.

On SignedPermutation

FindStat's St001819.

Called as CombinatorialStat(x, "FlagDenertIndex"). The head's page has its examples.

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Distribution

Over SignedPermutations at each size, tallied here in your browser; sizes past 6 are not offered.

Sizes 1 to

FindStat St001819

The flag Denert index of a signed permutation.

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 $\sigma$.

Object	Value
[1]	0
[-1]	1
[1,2]	0
[2,1]	2
[-1,2]	1
[-2,1]	3
[1,-2]	1
[2,-1]	3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001819 has the rest.