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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/63705


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/63705


    Title: 一個珠狀排列的公式
    A Formula for Calculating Necklace Permutations
    Authors: 薛麗姿
    Contributors: 李陽明
    薛麗姿
    Keywords: 波利亞計數定理
    伯恩賽定理
    置換群
    循環群
    正n邊形群
    循環指標式
    Date: 2013
    Issue Date: 2014-02-10 14:55:52 (UTC+8)
    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。
    The 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 .
    Reference: [1] Alan Tucker (2007,5th edition). Applied Combinatorics. John Wiley & Sons Inc.
    [2] John B. Fraleigh (2002,7th edition). A First Course In Abstract Algebra. Addison Wesley.
    [3] Ralph P. Grimaldi (1999,4th edition). Discrete And Combinatorial Mathematics. Addison Wesley.
    [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)。
    [5] 康明昌 (民77)。近世代數。台北市：聯經。
    [6] 蕭文強 (民83)。波利亞計數定理。新竹市：凡異。
    [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。
    [8] 孫航同 (民101)。一個環狀排列的公式。政大應數所碩士論文。
    [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。
    Description: 碩士
    國立政治大學
    應用數學系數學教學碩士在職專班
    100972010
    102
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0100972010
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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