On the Rogers-Selberg Identities and Gordon’s Theorem

Citation data:

CONFERENCE: Southeast Regional Meeting on Numbers (SERMON)

Southeast Regional Meeting on Numbers (SERMON)

Publication Year:
2009

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Repository URL:
https://works.bepress.com/andrew_sills/70; https://digitalcommons.georgiasouthern.edu/math-sci-facpres/24
Author(s):
Sills, Andrew
Tags:
Rogers-Selberg identities; Gordon's theorem; Mathematics; Academics, Science & Mathematics, Mathematical Sciences, Faculty Presentations
lecture / presentation description
The Rogers-Ramanujan 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 Rogers-Ramanujan 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 Rogers-Selberg identities. I will discuss a bijection between two relevant classes of integer partitions that explains the connection between Gordon and Rogers-Selberg. This work appeared in JCTA 115 (2008) 67-83.