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
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by A. K. Agarwal

Proc. Amer. Math. Soc. 107 (1989), 561-567

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

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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.

References

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