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Abstract
Balogh, Liu, Sharifzadeh and Treglown [Journal of the European Mathematical Society, 2018] recently gave a sharp count on the number of maximal sum-free subsets of {1, . . . , n}, thereby answering a question of Cameron and Erd ̋os. In contrast, not as much is known about the analogous problem for finite abelian groups. In this paper we give the first sharp results in this direction, determining asymptotically the number of maximal sum-free sets in both the binary and ternary spaces Zk2 and Zk3. We also make progress on a conjecture of Balogh, Liu, Sharifzadeh and Treglown concerning a general lower bound on the number of maximal sum-free sets in abelian groups of a fixed order. Indeed, we verify the conjecture for all finite abelian groups with a cyclic component of size at least 3084. Other related results and open problems are also presented.
Original language | English |
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Article number | P2.32 |
Pages (from-to) | 1-24 |
Number of pages | 24 |
Journal | The Electronic Journal of Combinatorics |
Volume | 29 |
Issue number | 2 |
DOIs | |
Publication status | Published - 20 May 2022 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics
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Dive into the research topics of 'On maximal sum-free sets in abelian groups'. Together they form a unique fingerprint.Projects
- 1 Finished
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Matchings and tilings in graphs
Engineering & Physical Science Research Council
1/03/21 → 29/02/24
Project: Research Councils