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Alignments on Permutation ​

Pairs i, j of arcs of the permutation diagram that align.

On Permutation

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

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FindStat St000222

The number of alignments in the permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000222 has the rest.