### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Results on Ghost Series and Motivated Proofs for Overpartition Identities

Speaker: **Collin Takita**, Ursinus College

Date: Thursday, December 10, 2015 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract

We give what we call a "motivated proof" of the overpartition analogue ofĂ‚ Bressoud's Theorem, originally proved by Lovejoy, et al. and Chen, et al. The first such "motivated proof," a proof of the Rogers-Ramanujan identities, was given by Andrews and Baxter. This work was later extended by many authors to Gordon's partition identities (by Lepowsky and Zhu), the Gollnitz-Gordon identities (by Coulson, Kanade, Lepowsky, McRae, Qi, Russell, Sadowski), and the Andrews-Bressoud identities (by Kanade, Lepowsky, Russell, Sills). Our proof is in the spirit of the work by Kanade, Lepowsky, Russell, and Sills, where certain new series, called "ghost series," are introduced in order to prove an Empirical Hypothesis and to give a proof of the overpartition analogue of Bressoud's Theorem. In the process, we show that the Ghost Series also have their own combinatorial interpretations. This is joint work with Matthew Russell and Christopher Sadowski.

See: http://www.math.rutgers.edu/~russell2/expmath/