Partitions With Early Conditions and Mock Theta Functions
March 31 2015, 1:55 — 2:45pm at LIT 368.
This talk is devoted to joint work with Stephen Hill (a Penn State undergraduate). In 1961, Basil Gordon proved a sweeping generalization of the Rogers-Ramanujan identities. His theorem may be broadly characterized as identifying the generating function for partitions having specified difference conditions on the parts with the quotient of two theta functions. We shall provide a new class of partitions (similar to those studied by Gordon) where the generating function is identified with the quotient of a Hecke-type theta series divided by the Dedekind eta function. The simplest case is related to one of the fifth order mock theta functions of Ramanujan. The partitions in question are similar in kind to those described in two earlier papers, Partitions with initial repetitions, Acta Math. Sinica, English Series, 25(2009), 1437-1442, and, Partitions with early conditions, Advances in Combinatorics Waterloo Workshop in Computer Algebra, W80 May. 26-29, 2011.