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.
Originalsprache | englisch |
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Titel | Proceedings of the 31st Conference on Formal Power Series and Algebraic Combinatorics |
Untertitel | Séminaire Lotharingien de Combinatoire |
Seitenumfang | 12 |
Band | 82B |
Publikationsstatus | Veröffentlicht - 2019 |
Veranstaltung | FPSAC 2019 - Ljubljana, Slowenien Dauer: 1 Juli 2019 → 5 Juli 2019 |
Konferenz
Konferenz | FPSAC 2019 |
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Land/Gebiet | Slowenien |
Ort | Ljubljana |
Zeitraum | 1/07/19 → 5/07/19 |