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On the structure of long zero-sum free sequences and \(n\)-zero-sum free sequences over finite cyclic groups. (English) Zbl 1400.11058

Summary: 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 \(n\geq 50\) 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 \(n\).

MSC:

11B50 Sequences (mod \(m\))
11B75 Other combinatorial number theory
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