Home > Events > Content
Lecture on "the Steep-Bounce Zeta Map in Parabolic Cataland"

Speaker: Wenjie Fang, Doctor, Université Gustave Eiffel

Date: June 11, 2020

Time: 4:30 p.m.

Location: Joining Zoom Meeting: ID 841 296 9209, Password: 0630

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences

Abstract:

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.

Bio:

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.