InitialRise on DyckPath
The length of the opening run of up steps.
Height equals the index exactly while every step so far has been an up step.
Called as CombinatorialStat(x, "InitialRise"). 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.
FindStat St000025
The number of initial rises of a Dyck path.
| Object | Value |
|---|---|
[] | 0 |
[1,0] | 1 |
[1,0,1,0] | 1 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000025 has the rest.