MiddleNonRunHeight on DyckPath
The height of the middle turning point: the middle one of the peaks and valleys, left to right.
Called as CombinatorialStat(x, "MiddleNonRunHeight"). 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 St001910
The height of the middle non-run of a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 0 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 0 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001910 has the rest.