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.
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Gao, W., Li, Y., Yuan, P. et al. On the structure of long zero-sum free sequences and n-zero-sum free sequences over finite cyclic groups. Arch. Math. 105, 361–370 (2015). https://doi.org/10.1007/s00013-015-0813-y
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DOI: https://doi.org/10.1007/s00013-015-0813-y