On the structure of n-zero-sum free sequences over cyclic groups of order n

Peng, Jiangtao; Gong, Qian; Sun, Fang; Wang, Linlin

doi:10.1142/s1793042114500663

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2023

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“…As a fundamental result in zero-sum theory, the following theorem has been used in many papers, see e.g. [4,5,7,12].…”

Section: Introductionmentioning

confidence: 99%

On Sequences Without Short Zero-Sum Subsequences

Zeng,

Yuan

2023

Electron. J. Combin.

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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 $\mathsf{h}(S)$, where $\mathsf{h}(S)$ 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 $\mathsf{h}(S)$. 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 $|\sum(S)|=2|S|-1<|G|$.

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“…As a fundamental result in zero-sum theory, the following theorem has been used in many papers, see e.g. [4,5,7,12].…”

Section: Introductionmentioning

confidence: 99%