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MidPointsOfOccurrencesOf321 on Permutation ​

Positions that are the middle of a 321 occurrence: neither a left-to-right maximum nor a right-to-left minimum.

On Permutation

Called as CombinatorialStat(x, "MidPointsOfOccurrencesOf321"). The head's page has its examples.

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Distribution

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FindStat St000371

The number of mid points of decreasing subsequences of length 3 in a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000371 has the rest.