Speaker: Wenjie Fang, Doctor, Université Gustave Eiffel
Date: June 11, 2020
Time: 4:30 p.m.
Sponsor: Research Center for Mathematics and Interdisciplinary Sciences
As a classical object, the Tamari lattice has many generalizations, including $\nu$-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 $\nu$-Tamari lattices for bounce paths $\nu$. 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.
Dr. Wenjie Fang completed his Ph.D. from Universitéde Paris 7 Denis Didero. He is currently maître de conférences of UniversitéGustave Eiffel. Wenjie does research in combinatorics and related fields, especially on enumeration and bijection.
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Edited by: Su Chang, Xie Tingting