Activity: Talk or presentation › Talk at workshop, seminar or course › Science to science
Tamari lattice is a partial order defined on objects counted by Catalan numbers, such as binary trees and Dyck paths. It is a well-studied object in combinatorics, with several generalizations. In this talk, we will see how intervals in these Tamari-like lattices are related to planar maps. More precisely, we discovered a bijection between non-separable planar maps and intervals in the generalized Tamari lattice, which naturally extends to a bijection between bridgeless planar maps and intervals in the original Tamari lattice. We will also discuss the consequences of these bijections in enumerative and structural studies of the related objects.