Name
Abstract | ||
|---|---|---|
As a classical object, the Tamari lattice has many generalizations, including ν-Tamari lattices and parabolic Tamari lattices. In this article, we unify these generalizations in a bijective fashion. We first prove that parabolic Tamari lattices are isomorphic to ν-Tamari lattices for bounce paths ν. We then introduce a new combinatorial object called “left-aligned colorable tree”, and show that it provides a bijective bridge between various parabolic Catalan objects and certain nested pairs of Dyck paths. As a consequence, we prove the Steep-Bounce Conjecture using a generalization of the famous zeta map in q,t-Catalan combinatorics. A generalization of the zeta map on parking functions, which arises in the theory of diagonal harmonics, is also obtained as a labeled version of our bijection. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.jcta.2020.105210 | Journal of Combinatorial Theory, Series A |
Keywords | Field | DocType |
Parabolic Tamari lattice,ν-Tamari lattice,Bijection,Left-aligned colorable tree,Zeta map | Diagonal,Tamari lattice,Combinatorics,Bijection,Lattice (order),Generalization,Isomorphism,Conjecture,Mathematics,Parabola | Journal |
Volume | ISSN | Citations |
172 | 0097-3165 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cesar Ceballos | 1 | 22 | 5.41 |
| Wenjie Fang | 2 | 28 | 7.68 |
| Henri Mühle | 3 | 2 | 5.14 |