Symmetric Complete Sum-free Sets in Cyclic Groups

We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in [0,13], answering a question of Cameron, and that the number of those contained in the cyclic group of order n is exponential in n. For primes p,...

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Bibliographic Details
Published in:Electronic notes in discrete mathematics 2017-08, Vol.61, p.585-591
Main Authors: Haviv, Ishay, Levy, Dan
Format: Article
Language:English
Subjects:
complete sets
cyclic groups
sum-free sets
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Summary:We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in [0,13], answering a question of Cameron, and that the number of those contained in the cyclic group of order n is exponential in n. For primes p, we provide a full characterization of the symmetric complete sum-free subsets of Zp of size at least (13−c)⋅p, where c>0 is a universal constant.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2017.07.011