Speaker:  Susanna Lang, U Kentucky

Title:  Rational Catalan Numbers and Associahedra

Abstract:

Classical Catalan numbers are known to count over 200 combinatorial objects, including Dyck paths, noncrossing partitions, and vertices of the classical associahedra. In this talk we discuss a generalization of the classical Catalan numbers and their connection with a class of simplicial complexes known as rational associahedra. We show rational associahedra have many nice properties, in particular they are shellable. This talk follows the paper "Rational Associahedra and Noncrossing Partitions" by Armstrong, Rhoades, and Williams.

This is Susanna Lang's Masters exam.