DownStepHeightProduct on DyckPath
The product, over the down steps, of the height each starts from.
Called as CombinatorialStat(x, "DownStepHeightProduct"). 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 St000038
The product of the heights of the descending steps of a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 1 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 2 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 4 |
[1,1,1,0,0,0] | 6 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000038 has the rest.