DiagonalStandardMonomialDegree on DyckPath
The degree of the standard monomial of the path relative to the diagonal boundary.
FindStat's St001508, as its Sage code walks the path. St001509, the same relative to the trivial lower boundary, is not adopted: its published code does not run.
Called as CombinatorialStat(x, "DiagonalStandardMonomialDegree"). 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 St001508
The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001508 has the rest.