A result on the size of iterated sumsets in ${\mathbb{Z}}^d$

Abstract

In this paper we give a different approach to determining the cardinality of $h$-fold sumsets $hA$ when $A\subset {\mathbb{Z}}^d$ has $d+2$ elements. This enables us to provide more general result with a shorter and simpler proof. We also obtain an upper bound for the value of $|hA|$ when $A\subset {\mathbb{Z}}^d$ is a set of $d+3$ elements with simplicial hull.

arXiv commentIt was noticed that the proof of the main Theorem could be improved to give a more general result. Also some motivating examples are provided

References in corpus (1)

• Khovanskii's theorem and effective results on sumset structure