| 置换群作用于一类映射集的等价类的计数 |
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| 引用本文： | 唐善刚.置换群作用于一类映射集的等价类的计数[J].山东大学学报(理学版),2021,56(8):67-75. |
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| 作者姓名： | 唐善刚 |
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| 作者单位： | 西华师范大学数学与信息学院, 四川 南充 637009 |
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| 基金项目： | 国家自然科学基金资助项目(11401480);四川省教育厅自然科学重点项目(17ZA0383) |
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| 摘 要： | 应用Burnside-Polya计数定理与容斥原理等组合分析方法研究置换群作用于一类映射集的等价类的计数,具体得到循环置换群与二面体置换群作用下的一类映射集的等价类的显式计数公式及其相关的平面环型错排、空间环型错排的计数公式以及组合恒等式,拓展了已有文献的研究结果。
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| 关 键 词： | 置换群 容斥原理 Burnside-Polya计数定理 映射 等价类 组合恒等式 |
Enumerations of equivalent classes with actions of permutation group on a class of mapping set |
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| TANG Shan-gang.Enumerations of equivalent classes with actions of permutation group on a class of mapping set[J].Journal of Shandong University,2021,56(8):67-75. |
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| Authors: | TANG Shan-gang |
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| Institution: | School of Mathematics and Information, China West Normal University, Nanchong 637009, Sichuan, China |
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| Abstract: | Enumerations of equivalent classes with action of permutation group on a class of mapping set are studied by using Burnside-Polya enumerating theorem, principle of inclusion-exclusion and other combinatorial analysis. Enumerations of equivalent classes and its plane circular alternating permutation enumerations, space circular alternating permutation enumerations and combinatorial identities with actions of cycle group and dihedral group on a class of mapping set are obtained. These results generalize some known results. |
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| Keywords: | permutation group principle of inclusion-exclusion Burnside-Polya enumerating theorem mapping equivalent class combinatorial identities |
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