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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/61993


    Title: 有關錯排列的探討
    A Study about Derangements
    Authors: 王思堯
    Contributors: 李陽明
    王思堯
    Keywords: 錯排列
    Derangements
    Date: 2013
    Issue Date: 2013-12-02 17:47:00 (UTC+8)
    Abstract: 在本論文中，令Dn是{1, 2,..., n}的錯排列所形成的集合，而讓dn代表Dn的個數。我們討論一個常用的遞迴關係式：dn=(n-1)(dn-1+dn-2)。針對這個公式，我們將會先給一個組合論證；而本文將提供一個更為簡潔的方式來證明這個遞迴關係式，就是構造出兩個函數，分別從類Dn-1和Dn-2的集合映射到Dn上，並且證明這兩個函數是對射的函數。

    本文第一章先對錯排列作一個簡單的介紹，第二章則說明我們錯排列之間的映射是如何製造出來的，並且證明這樣的映射是沒有問題的，第三章則提供其他錯排列遞迴關係式的資訊，讓其他有興趣的夥伴們能一起探討。
    Reference: 1.Claude Berge. Principles of Combinatorics. Academic Press, New York, 1971.
    2.Richard A. Brualdi. Introductory Combinatorics. North-Holland, New York, 1977.
    3.Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics. Addison-Wesley, 1989.
    4.Selmer M. Johnson, Generation of permutations by adjacent transposition. Math. Comp., 17:282-285, 1963.
    5.C. L. Liu. Introduction to Combinatorial Mathematics. McGraw-Hill Book Co., New York, 1968.
    6.John Riordan. An Introduction to Combinatorial Analysis. Princeton University Press, Princeton, N.J., 1980. Reprint of the 1958 edition.
    7.Fred S. Roberts. Applied Combinatorics. Prentice Hall Inc., Englewood Cliffs, NJ, 1984.
    8.Alan Tucker. Applied Combinatorics. John Wiley & Sons Inc., New York, 1980.
    9.洪聰於，錯排列的對射證明，國立政治大學應用數學系碩士論文.，1994。
    Description: 碩士
    國立政治大學
    應用數學研究所
    100751002
    102
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0100751002
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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