Mathematical Sciences: Faculty Presentations (1991-2022)
On the Rogers-Selberg Identities and Gordon’s Theorem
Document Type
Presentation
Presentation Date
4-18-2009
Copyright
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Abstract or 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.
Sponsorship/Conference/Institution
Southeast Regional Meeting on Numbers (SERMON)
Location
Greensboro, NC
Recommended Citation
Sills, Andrew V..
2009.
"On the Rogers-Selberg Identities and Gordon’s Theorem."
Mathematical Sciences: Faculty Presentations (1991-2022).
Presentation 24.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/24