Ian Cavey (UMass): q,t-Catalan combinatorics and domino tilings

The q,t-Catalan numbers are sums over Dyck paths, weighted by statistics called area and dinv. These combinatorial objects and their relatives come from the study of certain symmetric functions called Macdonald polynomials. I will discuss a variant of the q,t-Catalan numbers that are weighted sums over certain nested families of paths. These nested families of paths are in bijection with domino tilings of certain regions in the plane. Using the machinery of “domino shuffling,” one can give an explicit product formula in the special case corresponding to domino tilings of the Aztec diamond. This is joint work with Yi-Lin Lee.