北京邮电大学学报

  • EI核心期刊

北京邮电大学学报 ›› 2011, Vol. 34 ›› Issue (4): 47-50.doi: 10.13190/jbupt.201104.47.144

• 论文 • 上一篇    下一篇

差集和差集偶理论的轨道规律

贾彦国,纪永峰,任富争,许成谦   

  1. 燕山大学 信息科学与工程学院, 秦皇岛 066004
  • 收稿日期:2010-09-09 修回日期:2011-04-02 出版日期:2011-08-28 发布日期:2011-07-18
  • 通讯作者: 任富争 E-mail:rfz0374@163.com
  • 基金资助:

    国家自然科学基金项目(60872061, 60971126); 河北省教育厅科学研究计划项目(2008151)

Research on the Orbit Discipline of Difference Set and Difference Set Pairs

  • Received:2010-09-09 Revised:2011-04-02 Online:2011-08-28 Published:2011-07-18
  • Contact: Fu-Zheng REN E-mail:rfz0374@163.com
  • Supported by:

    National Natural Science Foundation of China under Grant No. 90920006;National Natural Science Foundation of China under Grant No. 90920006

摘要:

关于差集或差集偶的乘子定理和乘子猜想,可以通过轨道的方法判定差集或差集偶的不存在性. 通过对素数p在v阶Abel群G上所生成的轨道规律的研究,提出了阶数v是单个素数和2个素数乘积形式的轨道长度和轨道数的规律,并证明了其正确性. 利用这种规律可快速判断出特定参数的差集或差集偶的不存在性.

关键词: 差集, 差集偶, 乘子定理, 乘子猜想, 轨道

Abstract:

According to difference set and difference set pairs multiplier theorem and multiplier conjecture, the method by onorbit can determine the nonexistence of difference set and difference set pairs. The orbit created by prime p in Abelian group G by order v is discussed. Two kinds of orbit discipline are presented and proved. The one is order described by only one prime number, another is order described by the product of two prime numbers. Nonexistence of difference set or difference set pairs with the specific parameters is determined.

Key words: difference set, difference set pairs, multiplier theorem, multiplier conjecture, orbit