The Generalized Catalan Number
by Eric SOMMERS (University of Massachusetts)
Abstract:
The usual Catalan numbers arise in many contexts in mathematics (for
example, as the number of triangulations of a convex (n+2)-gon). In
this talk, I will define the generalized Catalan number for each root
system and then describe three objects which are enumerated by this number:
noncrossing partitions, ideals in the poset of positive roots, and
clusters. In the latter part of the talk, I will discuss two
applications of these ideas to representation theory.