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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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New combinatorial interpretations of two analytic identities
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by A. K. Agarwal PDF
Proc. Amer. Math. Soc. 107 (1989), 561-567 Request permission

Abstract:

Two generalized partition theorems involving partitions with "$n + 1$ copies of $n$" and " $n + 2$ copies of $n$", respectively, are proved. These theorems have potential of yielding infinite Rogers-Ramanujan type identities on MacMahon’s lines. Five particular cases are also discussed. Among them three are known and two provide new combinatorial interpretations of two known $q$-identities.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 561-567
  • MSC: Primary 05A19; Secondary 05A15, 05A17, 11P57
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0979216-7
  • MathSciNet review: 979216