FirstDownStepPosition on DyckPath

The position of the first down step.

On DyckPath

Called as CombinatorialStat(x, "FirstDownStepPosition"). 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 St000439

The position of the first down step of a Dyck path.

Object	Value
[1,0]	2
[1,0,1,0]	2
[1,1,0,0]	3
[1,0,1,0,1,0]	2
[1,0,1,1,0,0]	2
[1,1,0,0,1,0]	3
[1,1,0,1,0,0]	3
[1,1,1,0,0,0]	4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000439 has the rest.