Alladi Ramakrishnan Hall

Tamari Lattice and its Extensions - 2

Xavier Viennot

University of Bordeaux

Tamari lattice can also be defined with Dyck paths (or ballot paths above the diagonal). In relation with the dimension of the so-called higher diagonal coinvariant. F.Bergeron
introduced the m-Tamari lattice for every integer m, corresponding to paths above a line
with slope 1/m. It was an open problem to extend Tamari lattice to the so-called "rational Catalan combinatorics », i.e. to paths above a line will rational slope a/b. I will finish the talk by defining extensions of Tamari lattice, far more general that just paths above the line a/b (join work with L.-F. Préville-Ratelle).This work involves  algorithmic bijections between binary trees and pair of paths (or staircase polygons).