Name
Abstract | ||
|---|---|---|
An m-ballot path of size n is a path on the square grid consisting of north and east steps, starting at (0,0), ending at (mm, n), and never going below the ling {x = my}. The set of these paths can be equipped with a lattice structure, called the m-Tamari lattice and denoted T-n((m)), which generalizes the usual Tamari lattice T-n obtained when m = 1. We prove that the number of intervals in this lattice is m + 1/n(mn + 1)((m + 1)(2)n+m n - 1). This formula was recently conjectured by Bergeronin connection with the study of diagonal coinvariant spaces. The case m = 1 was proved a few years ago by Chapoton. Our proof is based on a recursive description of intervals, which translates into a functional equation satisfied by the associated generating function. The solution of this equation is an algebraic series, obtained by a guess-and-check approach. Finding a bijective proof remains an open problem. |
Year | Venue | DocType |
|---|---|---|
2012 | ELECTRONIC JOURNAL OF COMBINATORICS | Journal |
Volume | Issue | ISSN |
18.0 | 2.0 | 1077-8926 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mireille Bousquet-mélou | 1 | 421 | 56.28 |
| Éric Fusy | 2 | 198 | 21.95 |
| Louis-francois Preville-ratelle | 3 | 1 | 0.69 |