Minimal zero sum sequences of length four over finite cyclic groups
type: Item
instance of: scholarly article
title: Minimal zero sum sequences of length four over finite cyclic groups
zbMATH Open document ID: 1204.11021
author: Chris Plyley
author: Pingzhi Yuan
author: Xiangneng Zeng
author: Yuanlin Li
published in: Journal of Number Theory
publication date: 2010-07-22T00:00:00Z
review text: Let \(C_n\) be an additive cyclic group of order \(n\). Let \(S=g_1 \dots g_k\) be a minimal zero-sum sequence over \(C_n\), i.e., \(\sum_{i=1}^k g_i = 0\) yet \(\sum_{i \in I} g_i \neq 0\) for every proper and non-empty subset of \(\{1, \dots, k\}\). The sequence is said to have index \(1\) if there exist a generating element \(e\) of \(C_n\) and \(1 \leq a_i \leq n \) such that \(g_i = a_i e\) for each \(i\) and \(\sum_{i=1}^k a_i = n\). In view of various earlier results on minimal zero-sum sequences of index \(1\) the following question is relevant: Suppose \(n\) is co-prime to \(6\) and \(k=4\). Does it follow that the index of \(S\) is \(1\) ? In the paper under review a partial answer is given. Namely, it is proved that if \(n\) is a prime power co-prime to \(6\) and \(k=4\), then it follow that the index of \(S\) is \(1\).
Mathematics Subject Classification ID: 11B30
Mathematics Subject Classification ID: 11B50
zbMATH DE Number: 5759071
zbMATH Keywords: zero-sum problem
zbMATH Keywords: minimal zero-sum sequence
reviewed by: Wolfgang A. Schmid
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.12.005
OpenAlex ID: W2568097895
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DOI: 10.1016/J.JNT.2009.12.005
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description: scientific article; zbMATH DE number 5759071