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OccurrencesOf14Dash2Dash3Or14Dash3Dash2 on Permutation ​

Adjacent ascents p(i) < p(i+1) with two later entries between them, in either order, counted in pairs.

On Permutation

Called as CombinatorialStat(x, "OccurrencesOf14Dash2Dash3Or14Dash3Dash2"). The head's page has its examples.

Live

Distribution

Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.

FindStat St000709

The number of occurrences of 14-2-3 or 14-3-2.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000709 has the rest.