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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

New combinatorial interpretations of two analytic identities


Author: A. K. Agarwal
Journal: Proc. Amer. Math. Soc. 107 (1989), 561-567
MSC: Primary 05A19; Secondary 05A15, 05A17, 11P57
MathSciNet review: 979216
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0979216-7
PII: S 0002-9939(1989)0979216-7
Keywords: Partitions, weighted differences, $ q$-identities, combinatorial interpretations
Article copyright: © Copyright 1989 American Mathematical Society