On the structure of sequences with forbidden zero-sum subsequences

Abstract

We study the structure of longest sequences in ${{\mathbb Z}}_n^d$ which have no zero-sum subsequence of length $n$ (or less). We prove, among other results, that for $n=2^a$ and $d $ arbitrary, or $n=3^a$ and $d=3$, every sequence of $c(n,d)(n-1)$ elemen