Penn Arts & Sciences Logo

Wednesday, October 4, 2006 - 3:00pm

Andrew Sills

Rutgers University

Location

West Chester University

Anderson Hall # 108

Refreshment will be served in the Students Lounge after the talk

The Rogers-Ramanujan identities are famous in mathematics not only for their intrinsic beauty, but also for their appearance in analysis, number theory, combinatorics, Lie algebras, and statistical mechanics. In the 1940's, W.N. Bailey discovered a mathematical result (now known as ``Bailey's lemma") which can be used to prove the Rogers-Ramanujan identities easily, and to discover many identities of similar type via ``Bailey pairs." Bailey's student, L.J. Slater, found about 90 Bailey pairs, which she use to produce a list of 130 Rogers-Ramanujan type identities. I have recently found, however, that these 90 Bailey pairs of Slater are not isolated results. In fact, using just three generalized ``multiparameter Bailey pairs", and associated $q$-difference equations, I was able recover more than half of Slater's list. Furthermore, this more unified perspective made it possible to discover many new identities and provide natural combinatorial interpretations for many of the new and old identities.