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NonRecords on Permutation ​

Positions that are none of a left-to-right maximum or minimum, or a right-to-left maximum or minimum.

On Permutation

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

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Distribution

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

FindStat St001715

The number of non-records in a permutation.

ObjectValue
[1]0
[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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001715 has the rest.