置换群作用下的一类等间距环型排列的计数

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中图分类号：0157.1 文献标志码：A 文章编号：1673-5072（2025）05-0487-05

Enumeration of a Class of Equally Spaced Circular Permutations with Permutation Group Actions

TANG Shan-gang

（Schoolof Mathematics& Information，China West Normal University，Nanchong Sichuan 637009，China）

Abstract：Enumeration of linear permutations and circular permutations is a popular research field in combinatorics.By introducing the dihedral group to the equivalence class generated by a class of equally spaced mapping set，the definition of the equally spaced circular permutations on infinite duplicate set is given.And then，the explicit enumerative formulas of the equall spaced circular permutations on infinite duplicate set are obtained by using some combinatorial analysis methods such as Burnside-Polya enumerative theorem and the method of integer number theory，which further enriches the research results of enumerations of circular permutation.

Keywords ：permutation group ; equivalence relation; equivalence class;equally spaced circular permutations;Burnside-Polya enumerative theorem

计数组合[1是组合数学的一个研究分支。（剩余5716字）