On sequences without short zero-sum subsequences

Let G be a finite abelian group. It is well known that every sequence S over G of length at least |G| contains a zero-sum subsequence of length at most h(S), where h(S) is the maximal multiplicity of elements occurring in S. It is interesting to study the corresponding inverse problem, that is to find information on the structure of the sequence S which does not contain zero-sum subsequences of length at most h(S). Under the assumption that |& sum;(S)|<min{|G|,2|S|-1}, Gao, Peng and Wang showed that such a sequence S must be strictly behaving. In the present paper, we explicitly give the structure of such a sequence S under the assumption that |& sum;(S)|=2|S|-1<|G|.