中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (5): 137-144.doi: 10.13471/j.cnki.acta.snus.2019.05.017

• 论文 • 上一篇    下一篇

与群作用于集合的等价类计数有关的组合恒等式

唐善刚   

  1. 西华师范大学数学与信息学院,四川 南充 637009
  • 收稿日期:2018-11-30 出版日期:2019-09-25 发布日期:2019-09-25

Combinatorial identities for enumerations of equivalent classes with action of group on set

TANG Shangang   

  1. School of Mathematics and Information, China West Normal University, Nanchong 637009, China
  • Received:2018-11-30 Online:2019-09-25 Published:2019-09-25

摘要:

应用Burnside-Polya计数方法与容斥原理等组合分析方法研究一类与群作用于集合的等价类的计数有关的组合恒等式,具体得到恒等群、循环群与二面体群作用下的一类映射的等价类的计数有关的组合恒等式,拓展了已有文献的研究结果。

关键词: 群作用于集合, 容斥原理, Burnside-Polya计数法, 映射, 等价类, 组合恒等式

Abstract:

By using Burnside-Polya enumerating method, principle of inclusion-exclusion and other combinatorial analysis, a class of combinatorial identities for equivalent classes with action of group on set are studied. Some combinatorial identities for enumerations of equivalent classes of a class of mapping under identical transformation group and cycle group and dihedral group actions are obtained. These results generalize some known results.

Key words: action of group on set, principle of inclusion-exclusion, Burnside-Polya enumerating method, mapping, equivalent class, combinatorial identities

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