On the Rogers-Selberg Identities and Gordon’s Theorem
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.
Southeast Regional Meeting on Numbers (SERMON)
"On the Rogers-Selberg Identities and Gordon’s Theorem."
Mathematical Sciences Faculty Presentations.