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A Truncated Theta Identity of Gauss and Overpartitions into Odd Parts

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Abstract

We examine two truncated series derived from a classical theta identity of Gauss. As a consequence, we obtain two infinite families of inequalities for the overpartition function \(\overline{p_o}(n)\) counting the number of overpartitions into odd parts. We provide partition-theoretic interpretations of these results.

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Acknowledgements

The authors appreciate the anonymous referees for their comments on the original version of this paper.

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Authors and Affiliations

  1. Academy of Romanian Scientists, Ilfov 3, Sector 5, Bucharest, Romania

    Mircea Merca

  2. Department of Mathematics, East China Normal University, 500 Dongchuan Road, Shanghai, 200241, People’s Republic of China

    Chun Wang

  3. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Ae Ja Yee

Authors
  1. Mircea Merca
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  2. Chun Wang
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  3. Ae Ja Yee
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Corresponding author

Correspondence to Mircea Merca.

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Dedicated to Professor George E. Andrews

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Chun Wang was partially supported by the outstanding doctoral dissertation cultivation plan of action (No. YB2016028).

Ae Ja Yee was partially supported by a Grant (\(\#\)280903) from the Simons Foundation.

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Merca, M., Wang, C. & Yee, A.J. A Truncated Theta Identity of Gauss and Overpartitions into Odd Parts. Ann. Comb. 23, 907–915 (2019). https://doi.org/10.1007/s00026-019-00442-x

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  • DOI: https://doi.org/10.1007/s00026-019-00442-x

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