BoxWeight on DyckPath
The product, over the up steps, of one more than the number of down steps before it.
Follows FindStat's Sage code and its data, not its description: the description gives 4 for the path UUDD, the code and every stored value give 1.
Called as CombinatorialStat(x, "BoxWeight"). 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 St001808
The box weight or horizontal decoration of a Dyck path.
| Object | Value |
|---|---|
[1,0,1,0] | 2 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 6 |
[1,0,1,1,0,0] | 4 |
[1,1,0,0,1,0] | 3 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 1 |
[1,0,1,0,1,0,1,0] | 24 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001808 has the rest.