Peaks on DyckPath

Occurrences of an up step immediately followed by a down step.

On DyckPath

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

Live

Also on

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

FindStat St000015

The number of peaks of a Dyck path.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000015 has the rest.

FindStat St001068

The number of torsionless simple modules in the linear Nakayama algebra corresponding to a Dyck path.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001068 has the rest.