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Combinatorial and Additive Number Theory, New York Number Theory Seminar

Combinatorial and Additive Number Theory, New York Number Theory Seminar

CANT 2015, CANT 2016: Combinatorial and Additive Number Theory II pp 9–23Cite as

Open Problems About Sumsets in Finite Abelian Groups: Minimum Sizes and Critical Numbers

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 220)

Abstract

For a positive integer h and a subset A of a given finite abelian group, we let hA, \(h \hat{\;} A\), and \(h_{\pm }A\) denote the h-fold sumset, restricted sumset, and signed sumset of A, respectively. Here we review some of what is known and not yet known about the minimum sizes of these three types of sumsets, as well as their corresponding critical numbers. In particular, we discuss several new open direct and inverse problems.

Keywords

  • Additive combinatorics
  • Finite abelian group
  • Sumset
  • Critical number

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  • DOI: 10.1007/978-3-319-68032-3_2
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Notes

  1. 1.

    Note that \(\lfloor 2 \sqrt{n-2} \rfloor +1=n/p+p\) in this case.

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Authors and Affiliations

  1. Department of Mathematics, Gettysburg College, Gettysburg, PA, 17325-1486, USA

    Béla Bajnok

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  1. Béla Bajnok
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Correspondence to Béla Bajnok .

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  1. Department of Mathematics, Lehman College (CUNY), Bronx, New York, USA

    Melvyn B. Nathanson

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Bajnok, B. (2017). Open Problems About Sumsets in Finite Abelian Groups: Minimum Sizes and Critical Numbers. In: Nathanson, M. (eds) Combinatorial and Additive Number Theory II. CANT CANT 2015 2016. Springer Proceedings in Mathematics & Statistics, vol 220. Springer, Cham. https://doi.org/10.1007/978-3-319-68032-3_2

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