WeaklyAboveLatticePathCount on DyckPath
The up-and-down paths of the same length, ending anywhere, that stay weakly above this path.
The paths need not return to the axis: 2^n for the highest path, the central binomial coefficient for the zigzag.
Called as CombinatorialStat(x, "WeaklyAboveLatticePathCount"). 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 St001361
The number of lattice paths of the same length that stay weakly above a Dyck path.
| Object | Value |
|---|---|
[1,0] | 2 |
[1,0,1,0] | 6 |
[1,1,0,0] | 4 |
[1,0,1,0,1,0] | 20 |
[1,0,1,1,0,0] | 16 |
[1,1,0,0,1,0] | 14 |
[1,1,0,1,0,0] | 12 |
[1,1,1,0,0,0] | 8 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001361 has the rest.