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arXiv · 1703.04118

Symmetric Complete Sum-free Sets in Cyclic Groups

Ishay Haviv·Dan Levy
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Abstract

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 $[0,\frac{1}{3}]$, 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 $\mathbb{Z}_p$ of size at least $(\frac{1}{3}-c) \cdot p$, where $c>0$ is a universal constant.

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Ishay Haviv, Dan Levy. 2017-05-01. Symmetric Complete Sum-free Sets in Cyclic Groups. https://arxiv.org/abs/1703.04118

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