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arXiv:1304.3650 [math.CO]AbstractReferencesReviewsResources

A note on a sumset in $\mathbb{Z}_{2k}$

Octavio A. Agustín-Aquino

Published 2013-04-12, updated 2015-09-11Version 3

Let $A$ and $B$ be additive sets of $\mathbb{Z}_{2k}$, where $A$ has cardinality $k$ and $B=v.\complement A$ with $v\in\mathbb{Z}_{2k}^{\times}$. In this note some bounds for the cardinality of $A+B$ are obtained, using four different approaches. We also prove that in a special case the bound is not sharp and we can recover the whole group as a sumset.

Categories: math.CO
Subjects: 11B13, 11L07
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