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DescentsOrRecoils on Permutation ​

Indices i < n that are a descent of p or a recoil.

On Permutation

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

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Distribution

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FindStat St000831

The number of indices that are either descents or recoils.

ObjectValue
[1,2]0
[2,1]1
[1,2,3]0
[1,3,2]1
[2,1,3]1
[2,3,1]2
[3,1,2]2
[3,2,1]2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000831 has the rest.