Hills on DyckPath
Peaks at height 1 — an up step from the axis immediately followed by a down step.
Hills of size one: a hill of size k is k up steps then k down steps from the axis (HillsOfSizeTwo, HillsOfSizeThree).
Called as CombinatorialStat(x, "Hills"). 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 St000674
The number of hills of a Dyck path.
| Object | Value |
|---|---|
[1,0,1,0] | 2 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 0 |
[1,0,1,0,1,0,1,0] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000674 has the rest.