On the RogersSelberg Identities and Gordon’s Theorem
 Citation data:

CONFERENCE: Southeast Regional Meeting on Numbers (SERMON)
Southeast Regional Meeting on Numbers (SERMON)
 Publication Year:
 2009
 Researchers:
 Andrew V. Sills
 Repository URL:
 https://works.bepress.com/andrew_sills/70; https://digitalcommons.georgiasouthern.edu/mathscifacpres/24
 Author(s):
 Tags:
 RogersSelberg identities; Gordon's theorem; Mathematics; Academics, Science & Mathematics, Mathematical Sciences, Faculty Presentations
lecture / presentation description
The RogersRamanujan identities are among the most famous in the theory of integer partitions. For many years, it was thought that they could not be generalized, so it came as a big surprise when Basil Gordon found an infinite family of partition identities that generalized RogersRamanujan in 1961. Since the publication of Gordon's result, it has been suspected that a certain special case of his identity should provide a combinatorial interpretation for a set of three analytic identities known as the RogersSelberg identities. I will discuss a bijection between two relevant classes of integer partitions that explains the connection between Gordon and RogersSelberg. This work appeared in JCTA 115 (2008) 6783.