In a recent paper by Curran and Goldmakher, the cardinality of $h$-fold sumsets $hA$ was given when $A\subset {\mathbb{Z}}^d$ has $d+2$ elements. In this paper we provide a different method for doing this and obtain a more general result.

We also obtain an upper bound for the value of $\left|hA\right|$ when $A\subset {\mathbb{Z}}^d$ is a set of $d+3$ elements with simplicial hull.

中文翻译：

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关于 ℤd 中迭代求和集大小的注释

在 Curran 和 Goldmakher 最近的一篇论文中，$H$-折叠总和$HA$被给予时$A\subset {\mathbb{Z}}^d$有$d+2$元素。在本文中，我们提供了一种不同的方法来执行此操作并获得更通用的结果。

我们还获得了值的上限$\left|HA\right|$什么时候$A\subset {\mathbb{Z}}^d$是一组$d+3$具有简单船体的元素。