$B_h$ Sequences in Higher Dimensions

Abstract

In this article we look at the well-studied upper bounds for $|A|$, where $A\subset{\Bbb N}$ is a $B_h$ sequence, and generalise these to the case where $A\subset{\Bbb N}^d$. In particular we give $d$-dimensional analogues to results of Chen, Jia, Graham and Green.