New combinatorial interpretations of two analytic identities

Agarwal, A. K.

doi:10.1090/S0002-9939-1989-0979216-7

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
DOI: https://doi.org/10.1090/S0002-9939-1989-0979216-7
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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