Valleys on Permutation

Interior positions with p(i-1) > p(i) < p(i+1).

On Permutation

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

Live

Also on

The same name on other carriers, each its own implementation: DyckPath.

FindStat St000353

The number of inner valleys of a permutation.

Object	Value
[1,2]	0
[2,1]	0
[1,2,3]	0
[1,3,2]	0
[2,1,3]	1
[2,3,1]	0
[3,1,2]	1
[3,2,1]	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000353 has the rest.