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Groups with few maximal sum-free sets
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Liu, Hong and Sharifzadeh, Maryam (2021) Groups with few maximal sum-free sets. Journal of Combinatorial Theory, Series A, 177 . 105333. doi:10.1016/j.jcta.2020.105333 ISSN 0097-3165.
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WRAP-Groups-few-maximal-sum-free-sets-Liu-2020.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (918Kb) | Preview |
Official URL: http://dx.doi.org/10.1016/j.jcta.2020.105333
Abstract
A set of integers is sum-free if it does not contain any solution for . Answering a question of Cameron and Erdős, Balogh, Liu, Sharifzadeh and Treglown recently proved that the number of maximal sum-free sets in is , where is the size of a largest sum-free set in . They conjectured that, in contrast to the integer setting, there are abelian groups G having exponentially fewer maximal sum-free sets than , where 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 such that almost all even order abelian groups G have at most maximal sum-free sets.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Number theory, Abelian groups, Sequences (Mathematics) | ||||||||||||
| Journal or Publication Title: | Journal of Combinatorial Theory, Series A | ||||||||||||
| Publisher: | Elsevier | ||||||||||||
| ISSN: | 0097-3165 | ||||||||||||
| Official Date: | January 2021 | ||||||||||||
| Dates: |
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| Volume: | 177 | ||||||||||||
| Article Number: | 105333 | ||||||||||||
| DOI: | 10.1016/j.jcta.2020.105333 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Date of first compliant deposit: | 25 September 2020 | ||||||||||||
| Date of first compliant Open Access: | 18 September 2021 | ||||||||||||
| RIOXX Funder/Project Grant: |
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