Abstract:
As a classical object, the Tamari lattice has many generalizations, including ν-Tamari lattices and parabolic Tamari lattices. In this talk, we unify these generalizations in a bijective fashion. We introduce a new combinatorial object 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. Under these bijections, that parabolic Tamari lattices are proved to be isomorphic to ν-Tamari lattices for bounce paths ν. As another consequence of our bijections, we prove the Steep-Bounce conjecture using a generalization of the famous zeta map in q,t-Catalan combinatorics. This is a joint work with Cesar Ceballos and Henri Mühle.
Steep-bounce zeta map in parabolic Cataland
11.12.2018 15:15 - 16:45
Organiser:
M. Drmota
Location: