Subsequence sums of a zero-sumfree sequence.
Let \(G\) be a finite additive Abelian group and let \(S=\{a_i\}_{i=1}^n\) be a finite sequence of elements of \(G\). Define \[ \Sigma(S)=\left\{\sum_{i\in I}a_i:\emptyset\neq I\subseteq\{1,\dots,n\}\right\}. \] The author shows the inequality \(|\Sigma(S)|\geq 2n-1\) provided that \(0\not\in\Sigma(S)\) and the group generated by \(a_1,\dots,a_n\) is not cyclic. He also determines when equality holds. This work generalizes previous results due to \textit{W.-D. Gao} and \textit{I. Leader} [J. Number Theory 120, No. 1, 26-32 (2006; Zbl 1192.11010)], and \textit{F. Sun} [Electron. J. Comb. 14, No. 1, Research Paper R52 (2007; Zbl 1206.11022)].
scientific article; zbMATH DE number 5523095
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