Bounce on DyckPath
The bounce statistic: the sum of the bounce points of the path that bounces from its end back toward the origin.
FindStat St000005. (Bounce, Area) and (Area, Dinv) share the same bivariate distribution (see dyck-statistics.test.ts).
Called as CombinatorialStat(x, "Bounce"). 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 St000005
The bounce statistic of a Dyck path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000005 has the rest.