Sequences not containing long zero-sum subsequences
Sequences not containing long zero-sum subsequences
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DOI：
10.1016/j.ejc.2005.06.001
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发表时间：
2006-08
期刊：
影响因子：
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通讯作者：
Weidong Gao;J. Zhuang
中科院分区：
文献类型：
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作者：
Weidong Gao;J. Zhuang
设G为有限阿贝尔群（加性），设D(G)表示G的Davenport常数，即G中D个元素的每一个序列（允许重复）都包含一个非空零和子序列的最小整数D。设S为G中|S|≥D(G)的元素序列。如果S不包含长度大于|S|−D(G)+1的零和子序列，则S为正常序列。本文得到了关于任意G的正规序列结构的一些结果。如果G=Cn⊕Cn和n满足一些研究得很好的性质，我们就确定了所有的正规序列。应用这些结果，我们得到了G中长度为|S|=|G|+D(G)−2的序列S的结构的一些结果，并且S不包含长度为|G|的零和子序列。
Let G be a finite abelian group (written additively), and let D(G) denote the Davenport’s constant of G, i.e. the smallest integer d such that every sequence of d elements (repetition allowed) in G contains a nonempty zero-sum subsequence. Let S be a sequence of elements in G with |S|≥D(G). We say S is a normal sequence if S contains no zero-sum subsequence of length larger than |S|−D(G)+1. In this paper we obtain some results on the structure of normal sequences for arbitrary G. If G=Cn⊕Cnand n satisfies some well-investigated property, we determine all normal sequences. Applying these results, we obtain correspondingly some results on the structure of the sequence S in G of length |S|=|G|+D(G)−2 and S contains no zero-sum subsequence of length |G|.