Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
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
We give what we call a "motivated proof" of the overpartition analogue ofÂ 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.