### 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: Conjecturing New Partition Identities with Computer Algebra

Speaker: **Matthew Russell**, Rutgers University

Date: Thursday, October 23, 2014 5:00pm

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

Abstract:

Rogers-Ramanujan identities and their numerous generalizations (Gordon, Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities concerned with the integers partitions. These identities (written in generating function form) are typically of the form ''product side'' equals ''sum side'', with the product side enumerating partitions obeying certain congruence conditions and the sum side obeying certain initial conditions and difference conditions (along with possibly other restrictions). We use symbolic computation to generate various such sum sides and then use Euler's algorithm to see which of them actually do produce elegant conjectured product sides. We not only rediscover many of the known identities but also discover some apparently new ones. Joint work with Shashank Kanade.

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