Catalan Structures for Weyl and Coxeter Groups

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

The proposal is to study four important combinatorial structures related to Catalan numbers (associahedra, non-crossing partitions, non-nesting partitions, Tamari lattices), some of which have recently been generalized from type A to all finite Weyl groups. The goal is to tie them together via bijections and understand their enumerative, algebraic, and topological properties in a unified way. The focus of the proposal is on objects central to the study of symmetry, and how it can occur "in nature", a subject known in mathematics as "representation theory". The proposal will hopefully deepen our understanding of such symmetry, by explaining more of the features that accompany it whenever it occurs, and possibly how we can exploit them.