TouchPointCount on DyckPath
Points where the path touches the axis — the returns.
The catalog carries both spellings; they are the same statistic, which is why both are defined rather than one aliased to the other.
Called as CombinatorialStat(x, "TouchPointCount"). 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 St000011
The number of touch points (or returns) of a Dyck path.
| Object | Value |
|---|---|
[] | 0 |
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 2 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000011 has the rest.