RunsOfLengthOne on DyckPath

Maximal runs of equal steps that are a single step.

On DyckPath

Counts runs of both kinds of step, up and down; FindStat's title, "single rises", is misleading.

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

Live

Distribution

Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.

Sizes 1 to

FindStat St001669

The number of single rises in a Dyck path.

Object	Value
[1,0]	2
[1,0,1,0]	4
[1,1,0,0]	0
[1,0,1,0,1,0]	6
[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]	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001669 has the rest.