On generalized Erdos-Ginzburg-Ziv constants of C-n(r)

doi:10.1016/j.disc.2018.12.018

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	On generalized Erdos-Ginzburg-Ziv constants of C-n(r)
	Han, Dongchun 1; Zhang, Hanbin 2
	2019-04-01
发表期刊	DISCRETE MATHEMATICS
ISSN	0012-365X
卷号	342 期号:4 页码:1117-1127
摘要	Let G be an additive finite abelian group with exponent exp(G) = n. For any positive integer k, the kth Erdos-Ginzburg-Ziv constant s(kn) (G) is defined as the smallest positive integer t such that every sequence S in G of length at least t has a zero-sum subsequence of length kn. It is easy to see that s(kn)(C-n(r)) >= (k + r)n - r where n, r is an element of N. Kubertin conjectured that the equality holds for any k >= r. In this paper, we prove the following results: (1) For every positive integer k >= 6, we have s(kn)(C-n(3)) = (k + 3)n + O(n/ln n). (2) For every positive integer k >= 18, we have s(kn)(C-n(4)) = (k + 4)n + O(n/ln n) (3) For n is an element of N, assume that the largest prime power divisor of n is p(a) for some a is an element of N. For any fixed r >= 5, if p(t) >= r for some t is an element of N, then for any k is an element of N we have s(kpn)(t)(C-n(r)) <= (kp(t) + r)n + cr n/ln n, where c(r) is a constant that depends on r. Our results verify the conjecture of Kubertin asymptotically in the above cases. (C) 2019 Elsevier B.V. All rights reserved.
关键词	Zero-sum theory Generalized Erdos-Ginzburg-Ziv constants
DOI	10.1016/j.disc.2018.12.018
语种	英语
资助项目	National Science Foundation of China[11671218] ; Fundamental Research Funds for the Central Universities[2682016CX121] ; China Postdoctoral Science Foundation[2017M620936]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000460718800023
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/33465
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Hanbin
作者单位	1.Southwest Jiaotong Univ, Dept Math, Chengdu 610000, Sichuan, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Han, Dongchun,Zhang, Hanbin. On generalized Erdos-Ginzburg-Ziv constants of C-n(r)[J]. DISCRETE MATHEMATICS,2019,342(4):1117-1127.
APA	Han, Dongchun,&Zhang, Hanbin.(2019).On generalized Erdos-Ginzburg-Ziv constants of C-n(r).DISCRETE MATHEMATICS,342(4),1117-1127.
MLA	Han, Dongchun,et al."On generalized Erdos-Ginzburg-Ziv constants of C-n(r)".DISCRETE MATHEMATICS 342.4(2019):1117-1127.