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AdmissibleInversionsPlusDescents on Permutation ​

ShareshianWachsAdmissibleInversions plus the descents.

On Permutation

Shareshian and Wachs's aid.

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

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Distribution

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FindStat St000868

The aid statistic in the sense of Shareshian-Wachs.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000868 has the rest.