Subsequence sums of a zero-sumfree sequence.
type: Item
instance of: scholarly article
title: Subsequence sums of a zero-sumfree sequence.
zbMATH Open document ID: 1170.20033
author: Pingzhi Yuan
published in: European Journal of Combinatorics
publication date: 2009-03-04T00:00:00Z
review text: 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)].
reviewed by: Zhi-Wei Sun
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11B50
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5523095
zbMATH Keywords: finite Abelian groups
zbMATH Keywords: zero-sum sequences
zbMATH Keywords: subset sums
MaRDI profile type: Publication
full work available at URL: j.ejc.2008.04.008
OpenAlex ID: W2035974373
cites work: Sums and \(k\)-sums in abelian groups of order \(k\)
cites work: Q5200682
cites work: On subsequence sums of a zero-sum free sequence
cites work: On the index of minimal zero-sum sequences over finite cyclic groups
DOI: 10.1016/J.EJC.2008.04.008
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description: scientific article; zbMATH DE number 5523095