Enumeration and Special Functions

Abstract

These are the notes for a series of lectures on $q$-series, orthogonalpolynomials, and symmetric functions and their connections toenumeration problems. The material ranges widely, including suchtopics as partition generating functions, the involution principle,the connection between $q$-Hermite polynomials and theRogers-Ramanujan identities, Hankel determinants, continued fractions,plane partitions, alternating sign matrices, and the Borweinconjecture. Open problems are sprinkled throughout. {For the entire collection see MR2022850 (2004f:33002).}