BounceDeficit on DyckPath
The binomial(n, 2) less the area and the bounce.
Called as CombinatorialStat(x, "BounceDeficit"). 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 St000376
The bounce deficit of a Dyck path.
| Object | Value |
|---|---|
[1,0,1,0] | 0 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 0 |
[1,0,1,0,1,0,1,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000376 has the rest.