Returns on DyckPath
Points where the path comes back to height 0.
Called as CombinatorialStat(x, "Returns"). 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.