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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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New weighted Rogers-Ramanujan partition theorems and their implications
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by Krishnaswami Alladi and Alexander Berkovich PDF
Trans. Amer. Math. Soc. 354 (2002), 2557-2577 Request permission

Abstract:

This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi’s celebrated triple product identity for theta functions, Sylvester’s famous refinement of Euler’s theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on successive ranks and replacing these with weighted Rogers-Ramanujan partitions, we obtain two new sets of theorems - a set of three theorems involving partitions into parts $\not \equiv 0, \pm i$ (mod 6), and a set of three theorems involving partitions into parts $\not \equiv 0, \pm i$ (mod 7), $i=1,2,3$.
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Additional Information
  • Krishnaswami Alladi
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
  • MR Author ID: 24845
  • Email: alladi@math.ufl.edu
  • Alexander Berkovich
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
  • MR Author ID: 247760
  • Email: alexb@math.ufl.edu
  • Received by editor(s): September 1, 2001
  • Published electronically: March 11, 2002
  • Additional Notes: Research of the first author supported in part by the National Science Foundation Grant DMS 0088975
    Research of the second author supported in part by a University of Florida CLAS Research Award
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2557-2577
  • MSC (2000): Primary 11P83, 11P81; Secondary 05A19
  • DOI: https://doi.org/10.1090/S0002-9947-02-02977-X
  • MathSciNet review: 1895193