AreaAboveBouncePath on DyckPath
The boxes between the path and its bounce path: the area less the area of the bounce path.
The bounce path is U^b1 D^b1 U^b2 D^b2 ... for the climbs b of the bounce walk, so its area is the sum of binomial(b, 2).
Called as CombinatorialStat(x, "AreaAboveBouncePath"). 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 St001584
The area statistic between a Dyck path and its bounce path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 0 |
[1,1,0,0,1,0] | 0 |
[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/St001584 has the rest.