FirstDescent on Permutation

The smallest descent position, or n when p is increasing.

On Permutation

FindStat St000654: p(n+1) = 0, so position n always descends.

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

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Distribution

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FindStat St000654

The first descent of a permutation.

Object	Value
[1,2]	2
[2,1]	1
[1,2,3]	3
[1,3,2]	2
[2,1,3]	1
[2,3,1]	2
[3,1,2]	1
[3,2,1]	1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000654 has the rest.