中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (2): 61-65.

• 论文 • 上一篇    下一篇

整数区间上长极小零和序列的结构

邓贵新1,曾祥能2   

  1. 1. 广西师范学院数学与统计科学学院,广西 南宁 530001;
    2. 中山大学中法核工程与技术学院, 广东 珠海 519082
  • 收稿日期:2017-08-23 出版日期:2018-03-25 发布日期:2018-03-25
  • 通讯作者: 曾祥能(1984年生),男; 研究方向: 组合数论;E-mail: junevab@163.com

The structure of long minimal zero-sum sequences over integral intervals

DENG Guixin1, ZENG Xiangneng2   

  1. 1. College of Mathematics and Statistics, Guangxi Teachers Education University, Nanning 530001, China;
    2. Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China
  • Received:2017-08-23 Online:2018-03-25 Published:2018-03-25

摘要:

有限交换群上的零和问题已经有很长研究历史,但是无限群上的零和问题的结论还比较少。主要研究整数集上的极小零和序列,得到了有限区间[-m,n]上所有长度不小于n+m-2的极小零和序列的结构。

关键词: 序列, 零和, 极小零和, Davenport常数

Abstract:

The research of zerosum problems over finite abelian groups has a long history, while there are only a few results concerned about zero-sum problems over infinite groups. The minimal zero-sum sequences over integers are studied. The structure of minimal zero-sum sequences over an integral interval [-m,n] whose lengths are at least n+m-2 is obtained.

Key words: sequences, zero-sum, minimal zero-sum, Davenport constant

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