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FlagWeakExcedance on SignedPermutation ​

Twice the weak excedances plus the negative entries.

On SignedPermutation

FindStat's St001817. A weak excedance is an entry p(i) >= i.

Called as CombinatorialStat(x, "FlagWeakExcedance"). 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.

FindStat St001817

The number of flag weak exceedances of a signed permutation.

ObjectValue
[1]2
[-1]1
[1,2]4
[2,1]2
[-1,2]3
[-2,1]1
[1,-2]3
[2,-1]3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001817 has the rest.