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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/56528


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/56528


    Title: 一個環狀排列的公式
    A Formula for Calculating Circular Permutations
    Authors: 孫航同
    Contributors: 李陽明
    孫航同
    Keywords: 波利亞計數定理
    伯恩賽定理
    置換群
    循環群
    循環指標式
    Date: 2012
    Issue Date: 2013-01-02 13:26:17 (UTC+8)
    Abstract: 這篇論文的目的，是要詳細解釋用波利亞計數方法來求解環狀排列問
    題的基本原理。為了達到這個目的，一開始對循環群的概念做了介紹。
    其次是伯恩賽定理的說明。接下來闡述波利亞計數方法的細節，最後
    藉由波利亞計數定理，設法建立一個可計算任何環狀排列問題的公式，
    並舉出實例，以顯示其實用價值。
    The purpose of this thesis is to explain the basic principle of the circular permutations using the Pólya`s enumeration method. Firstly , we introduce the concepts of the cyclic groups. Secondly , we illustrate the Burnside theorem , and then elaborate the Pólya`s enumeration method. Finally , we establish a formula that can calculate any type of the circular permutations by the Pólya`s enumeration method. And we also give several examples to reveal the results.
    Reference: [1] Alan Tucker：Applied Combinatorics (fifth edition) ,John Wiley & Sons , Inc (2007)
    [2] Richard A.Brualdi：Introductory Combinatorics (fourth edition) , Prentice-Hall (2004)
    [3] Joseph A. Gallian：Contemporary Abstract Algebra (seventh edition) ,Brooks/Cole(2010)
    [4] Jonathan L. Gross：Combinatorial Methods with Computer Applications , Chapman & Hall/CRC (2008)
    [5] Richard A. Mollin：Fundamental Number theory with Applications (second edition) , Chapman & Hall/CRC (2008)
    [6] Alan Slomson：An Introduction to Combinatorics (first edition), Chapman & Hall(1991)
    [7] Peter J.Cameron：Combinatorics：topics , techniques , algorithms ,Cambridge University Press (1994)
    [8] J.H.van Lint & R.M.Wilson：A Course in Combinatorics(second edition) , Cambridge University Press (2001)
    [9] 王世勛：不盡相異物的環狀排列公式， 政大應數所碩士論文 (2010)
    [10] 洪鵬凱：不盡相異物排列─著色與環狀排列問題，全國高中數學教學研討會論文集 (2007)
    [11] 潘承洞 潘承彪：初等數論，北京大學出版社 (1991)
    [12] 馮舜璽 羅平 裴偉東譯： 組合數學，機械工業出版社 (2005)
    [13] 蕭文強：波利亞計數定理，大連理工大學出版社 (2011)
    [14] 莫宗堅：代數學(上)，聯經出版公司 (1987)
    [15] 魏萬迪：初等組合數學導論，四川大學出版社 (1984)
    [16] 馮速：應用組合數學，人民郵電出版社 (2009)
    Description: 碩士
    國立政治大學
    應用數學系數學教學碩士在職專班
    99972001
    101
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0099972001
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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