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

Abstract

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.

References in corpus (1)

• A New Proof of Kemperman's Theorem