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A combinatorial study and comparison of partial theta identities of Andrews and Ramanujan

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Abstract

We provide a simple proof of a partial theta identity of Andrews and study the underlying combinatorics. This yields a weighted partition theorem involving partitions into distinct parts with smallest part odd which turns out to be a companion to a weighted partition theorem involving the same partitions that we recently deduced from a partial theta identity in Ramanujan’s Lost Notebook. We also establish some new partition identities from certain special cases of Andrews’ partial theta identity.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    Krishnaswami Alladi

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  1. Krishnaswami Alladi
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Correspondence to Krishnaswami Alladi.

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Dedicated to George Andrews on the occasion of his 70-th birthday.

Research supported in part by NSA Grants MSPF-06G-150 and MSPF-08G-154.

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Alladi, K. A combinatorial study and comparison of partial theta identities of Andrews and Ramanujan. Ramanujan J 23, 227–241 (2010). https://doi.org/10.1007/s11139-009-9188-7

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  • DOI: https://doi.org/10.1007/s11139-009-9188-7

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