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Gainesville International Number Theory Conference

ALLADI60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series pp 693–711Cite as

Overpartitions and Singular Overpartitions

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 221))

Abstract

Singular overpartitions, which were defined by George Andrews, are overpartitions whose Frobenius symbols have at most one overlined entry in each row. In his paper, Andrews obtained interesting combinatorial results on singular overpartitions, one of which relates a certain type of singular overpartition with a subclass of overpartitions. In this paper, we provide a combinatorial proof of Andrews’s result, which answers one of his open questions.

This paper is dedicated to Krishna Alladi on the occasion of his 60th birthday

S. Seo—The first author was partially supported by a research grant of Kangwon National University in 2015.

A.J. Yee—The second author was partially supported by a grant (#280903) from the Simons Foundation.

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References

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Acknowledgements

The authors would like to thank the anonymous referee for valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics Education, Kangwon National University, Chuncheon, Kangwon-do, 24341, Republic of Korea

    Seunghyun Seo

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

    Ae Ja Yee

Authors
  1. Seunghyun Seo
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  2. Ae Ja Yee
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Corresponding author

Correspondence to Ae Ja Yee .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, State College, Pennsylvania, USA

    George E. Andrews

  2. Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

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Seo, S., Yee, A.J. (2017). Overpartitions and Singular Overpartitions. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_38

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