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 ⊂ Z d has d + 2 elements. We also obtain the upper and lower bounds for the value of |hA| when A ⊂ Z d is a set of d + 3 elements with simplicial hull.