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Sum-free sets in abelian groups

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Abstract

We show that there is an absolute constant δ>0 such that the number of sum-free subsets of any finite abelian groupG is

$$\left( {2^{\nu (G)} - 1} \right)2^{\left| G \right|/2} + O\left( {2^{(1/2 - \delta )\left| G \right|} } \right)$$

whereν(G) is the number of even order components in the canonical decomposition ofG into a direct sum of its cyclic subgroups, and the implicit constant in theO-sign is absolute.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, 91904, Jerusalem, Israel

    Vsevolod F. Lev

  2. Department of Mathematics, Adam Mickiewicz University, Poznań, Poland

    Tomasz Łuczak

  3. Department of Mathematics, Christian Albrecht University, Kiel, Germany

    Tomasz Schoen

  4. Department of Discrete Mathematics, Adam Mickiewicz University, Poznan, Poland

    Tomasz Schoen

Authors
  1. Vsevolod F. Lev
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  2. Tomasz Łuczak
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  3. Tomasz Schoen
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Corresponding author

Correspondence to Vsevolod F. Lev.

Additional information

This author was partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany).

This author was partially supported by KBN grant 2 P03A 021 17.

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Lev, V.F., Łuczak, T. & Schoen, T. Sum-free sets in abelian groups. Isr. J. Math. 125, 347–367 (2001). https://doi.org/10.1007/BF02773386

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  • DOI: https://doi.org/10.1007/BF02773386

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