On the Rogers-Selberg Identities and Gordon’s Theorem

Research output: Contribution to conferencePresentation

Abstract

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.

Original languageAmerican English
StatePublished - Apr 18 2009
EventSoutheast Regional Meeting on Numbers (SERMON) -
Duration: Apr 18 2009 → …

Conference

ConferenceSoutheast Regional Meeting on Numbers (SERMON)
Period04/18/09 → …

Keywords

  • Gordon's theorem
  • Rogers-Selberg identities

DC Disciplines

  • Mathematics
  • Physical Sciences and Mathematics

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