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BabsonSteingrimssonStatisticPrime on Permutation ​

Descents plus the occurrences of the vincular patterns 13-2, 31-2 and 32-1.

On Permutation

FindStat's stat', after Babson and Steingrimsson.

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

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Distribution

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FindStat St000796

The stat' of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000796 has the rest.