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BoxedOccurrencesOf123 on Permutation ​

Occurrences of 123 with no other entry positioned between the first and last and valued between them.

On Permutation

Called as CombinatorialStat(x, "BoxedOccurrencesOf123"). 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 St001082

The number of boxed occurrences of 123 in a permutation.

ObjectValue
[1,2]0
[2,1]0
[1,2,3]1
[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/St001082 has the rest.