摘要
应用组合分析方法研究赋权有限集上的容斥原理,得到容斥原理的一些新命题,拓广并统一了已有文献的研究结果,将其用于恒等群、循环群与二面体群作用下的环形错排的计数,得到在恒等群、循环群与二面体群作用下的环形错排的显式计数公式与组合恒等式,拓展了已有文献的相关结果.
Principle of inclusion-exclusion on a weighted finite is studied by using combinatorial analysis method.Some new theorems for weighted principle of inclusion-exclusion are given and unify those of the previous studies.By using the new principle of inclusion-exclusion,enumerations for circular alternating permutation under identical transformation group and cycle group and dihedral group actions are studied. Some explicit enumerating formulas and combinatorial identities are obtained under identical transformation group and cycle group and dihedral group actions on circular alternating permutation. These results extend those of existing ones in some literatures.
作者
唐善刚
TANG Shan-gang(College of Mathematics and Information, China West Normal University, Nanchong 637009, Chin)
出处
《云南大学学报（自然科学版）》
CAS
CSCD
北大核心
2018年第3期405-414,共10页
Journal of Yunnan University(Natural Sciences Edition)
基金
四川省教育厅自然科学重点项目(17ZA0383)
国家自然科学基金(11401480)
关键词
容斥原理
恒等群
循环群
二面体群
环形错排
组合恒等式
principle of inclusion-exclusion
identical transformation group
cycle group
dihedral group
circular alternating permutation
combinatorial identities
