On Zero-sum Free Subsets of Length 7

Pingzhi Yuan, Xiangneng Zeng


Let $G$ be a finite additively written abelian group, and let $X$ be a subset of 7 elements in $G$. We show that if $X$ contains no nonempty subset with sum zero, then the number of the elements which can be expressed as the sum over a nonempty subsequence of $X$ is at least $ 24$.

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