On the structure of long zero-sum free sequences and n-zero-sum free sequences over finite cyclic groups

Abstract

In an additively written abelian group, a sequence is called zero-sum free if each of its nonempty subsequences has sum different from the zero element of the group. In this paper, we consider the structure of long zero-sum free sequences and n-zero-sum free sequences over finite cyclic groups \({\mathbb{Z}_n}\). Among which, we determine the structure of the long zero-sum free sequences of length between \({n/3+1 }\) and \({n/2}\), where \({n\ge 50}\) is an odd integer, and we provide a general description on the structure of n-zero-sum free sequences of length n + l, where \({\ell\geq n/p+p-2}\) and p is the smallest prime dividing n.