ProperlyBelowDyckPathCount on DyckPath
The Dyck paths of the same semilength weakly below this path, itself excluded.
Called as CombinatorialStat(x, "ProperlyBelowDyckPathCount"). 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 St000421
The number of Dyck paths that are weakly below a Dyck path, except for the path itself.
| Object | Value |
|---|---|
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 4 |
[1,0,1,0,1,0,1,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000421 has the rest.