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Descents on Permutation ​

Positions i with p(i) > p(i+1).

On Permutation

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

Live

FindStat St000021

The number of descents of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000021 has the rest.