On generalized Erdos-Ginzburg-Ziv constants of C-n(r)
文献类型：期刊论文
| 作者 | Han, Dongchun2; Zhang, Hanbin1 |
| 刊名 | DISCRETE MATHEMATICS
 |
| 出版日期 | 2019-04-01 |
| 卷号 | 342期号:4页码:1117-1127 |
| 关键词 | Zero-sum theory Generalized Erdos-Ginzburg-Ziv constants |
| ISSN号 | 0012-365X |
| DOI | 10.1016/j.disc.2018.12.018 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000460718800023 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [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.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Southwest Jiaotong Univ, Dept Math, Chengdu 610000, Sichuan, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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