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 general-izations 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 combinatorialobject called “left-aligned colored 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.
| Original language | English |
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| Title of host publication | Proceedings of the 31st Conference on Formal Power Series and Algebraic Combinatorics |
| Subtitle of host publication | Séminaire Lotharingien de Combinatoire |
| Number of pages | 12 |
| Volume | 82B |
| Publication status | Published - 2019 |
| Event | FPSAC 2019 - Ljubljana, Slovenia Duration: 1 Jul 2019 → 5 Jul 2019 |
Conference
| Conference | FPSAC 2019 |
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| Country/Territory | Slovenia |
| City | Ljubljana |
| Period | 1/07/19 → 5/07/19 |
Keywords
- parabolic Tamari lattice
- ν-Tamari lattice
- bijection
- left-aligned colorable tree
- zeta map