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Groups with few maximal sum-free sets
School of Mathematics, University of Birmingham, UK. (Discrete Mathematics)
2021 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 177, article id 105333Article in journal (Refereed) Published
Abstract [en]

A set of integers is sum-free if it does not contain any solution for x+y=z. Answering a question of Cameron and Erdős, Balogh, Liu, Sharifzadeh and Treglown recently proved that the number of maximal sum-free sets in {1,…,n} is Θ(2μ(n)/2), where μ(n) is the size of a largest sum-free set in {1,…,n}. They conjectured that, in contrast to the integer setting, there are abelian groups G having exponentially fewer maximal sum-free sets than 2μ(G)/2, where μ(G) denotes the size of a largest sum-free set in G.

We settle this conjecture affirmatively. In particular, we show that there exists an absolute constant c>0 such that almost all even order abelian groups G have at most 2(1/2−c)μ(G) maximal sum-free sets.

Place, publisher, year, edition, pages
Elsevier, 2021. Vol. 177, article id 105333
Keywords [en]
Sum-free sets, Abelian group
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-194731DOI: 10.1016/j.jcta.2020.105333ISI: 000578989800023Scopus ID: 2-s2.0-85091205275OAI: oai:DiVA.org:umu-194731DiVA, id: diva2:1658322
Funder
EU, Horizon 2020Available from: 2022-05-16 Created: 2022-05-16 Last updated: 2022-05-16Bibliographically approved

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Sharifzadeh, Maryam

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  • de-DE
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  • nn-NB
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