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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/63705
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dc.contributor.advisor李陽明zh_TW
dc.contributor.author薛麗姿zh_TW
dc.creator薛麗姿zh_TW
dc.date2013en_US
dc.date.accessioned2014-02-10T06:55:52Z-
dc.date.available2014-02-10T06:55:52Z-
dc.date.issued2014-02-10T06:55:52Z-
dc.identifierG0100972010en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/63705-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學系數學教學碩士在職專班zh_TW
dc.description100972010zh_TW
dc.description102zh_TW
dc.description.abstract這篇論文的目的，是要推廣學長的論文《一個環狀排列的公式》，欲藉由波利亞計數方法，來建立一個可計算任何珠狀排列問題的公式。為了達到這個目的，需要對循環群的概念及正n邊形群的結構做些介紹；並且說明伯恩賽定理及波利亞計數方法的內容；最後，利用波利亞計數定理，整理出珠狀排列的公式，並舉出實例，以顯示其實用價值。zh_TW
dc.description.abstractThe purpose of this thesis is to expand the conclusion of the thesis ”A Formula for Calculating Circular Permutations”, we want to establish a formula that can calculate any type of the necklace permutations by the Pólya’ s enumeration method . Firstly , we introduce the concept of the cyclic groups , and discuss the structure of the dihedral group . Secondly , we illustrate the Burnside theorem , and the Pólya’ s enumeration method . Finally , we conclude the formula for calculating necklace permutations . And we also give several examples to reveal the results .en_US
dc.description.tableofcontents致謝辭------------------------------------------------ I\n摘要-------------------------------------------------- II\nAbstract--------------------------------------------- III\n目次-------------------------------------------------- IV\n1. 前言----------------------------------------------- 1\n2. 理論方法-------------------------------------------- 2\n2.1 循環群 (cyclic group) 的簡介----------------------- 2\n2.2 循環節 (cycle) 的應用------------------------------ 6\n2.3 正 邊形群 (dihedral group) 的簡介------------------ 8\n2.4 循環指標式 (Cycle Index Polynomial)---------------- 13\n2.5 群對集合的作用-------------------------------------- 18\n2.6 伯恩賽定理 (Burnside theorem) 及其應用--------------- 23\n2.7 波利亞計數方法 (Pólya’ s enumeration method) 的綜合說明 28\n3. 實證----------------------------------------------- 33\n3.1 環狀排列的公式-------------------------------------- 33\n3.2 珠狀排列的公式-------------------------------------- 35\n3.3 珠狀排列的實例-------------------------------------- 38\n4. 結論----------------------------------------------- 49\n4.1 正多面體的對稱轉動----------------------------------- 49\n4.2 未來展望------------------------------------------- 52\n5. 參考文獻-------------------------------------------- 54\n中、英文名詞對照表--------------------------------------- 55zh_TW
dc.format.extent4592779 bytes-
dc.format.mimetypeapplication/pdf-
dc.language.isoen_US-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0100972010en_US
dc.subject波利亞計數定理zh_TW
dc.subject伯恩賽定理zh_TW
dc.subject置換群zh_TW
dc.subject循環群zh_TW
dc.subject正n邊形群zh_TW
dc.subject循環指標式zh_TW
dc.title一個珠狀排列的公式zh_TW
dc.titleA Formula for Calculating Necklace Permutationsen_US
dc.typethesisen
dc.relation.reference[1] Alan Tucker (2007,5th edition). Applied Combinatorics. John Wiley & Sons Inc.\n[2] John B. Fraleigh (2002,7th edition). A First Course In Abstract Algebra. Addison Wesley.\n[3] Ralph P. Grimaldi (1999,4th edition). Discrete And Combinatorial Mathematics. Addison Wesley.\n[4] 吳素美、范麗昌 (譯) (民91)。抽象代數導論 (原作者：John B. Fraleigh)。臺北市：五南。(原著出版年：2002)。\n[5] 康明昌 (民77)。近世代數。台北市：聯經。\n[6] 蕭文強 (民83)。波利亞計數定理。新竹市：凡異。\n[7] 王世勛 (民99)。不盡相異物的環狀排列公式。政大應數所碩士論文。\n[8] 孫航同 (民101)。一個環狀排列的公式。政大應數所碩士論文。\n[9] 洪鵬凱 (民96)。不盡相異物排列─著色與環狀排列的問題。全國高中數學教學研討會論文集。zh_TW
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item.openairecristypehttp://purl.org/coar/resource_type/c_46ec-
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