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UpperMiddleEntry on Permutation ​

The entry p(floor(n/2) + 1).

On Permutation

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

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Distribution

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FindStat St001806

The upper middle entry of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001806 has the rest.