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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/49451


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/49451


    Title: 不盡相異物的環狀排列公式
    A Formula on Circular Permutation of Nondistinct Objects
    Authors: 王世勛
    Wang,shyh shiun
    Contributors: 李陽明
    Li,young ming
    王世勛
    Wang,shyh shiun
    Keywords: 環狀排列
    不盡相異物
    circular permutation
    nondistinct objects
    indistinguishable objects
    Date: 2009
    Issue Date: 2010-12-08 11:44:57 (UTC+8)
    Abstract: n個物品之直線排列數與環狀排列數有對應關係，一般而言，具有K-循環節的直線排列之所有情形數若為 ，則 即為所對應的環狀排列數，亦即每K種直線排列對應到同一種環狀排列。本文將直線排列之所有情形依所具有的K-循環節之類別做分割，並導出具有K-循環節之直線排列之所有情形數之計數公式，假設直線排列依 -循環節， -循環節， ， -循環節分類依序有 種不同排列情形，則所有的環狀排列數 。
    There exists a correspondence between ordered arrangements and circular permutations. Generally speaking, suppose the number of ordered arrangements with K-recurring periods is S, then the number of circular permutations is , namely we may assigne each K cases of ordered arrangements with K-recurring periods to a case of circular permutations. This article partitions the total cases of ordered arrangements with indistinguishable objects by means of the different catagories of K-recurring periods and derives a formula to calculate the total number of ordered arrangements with K-recurring periods. Suppose the number of ordered arrangements with -recurring periods、 -recurring periods、 、 -recurring periods is respectively, then the total number of circular permutations is .
    Reference: [1]陳壽愷，民國63年(1974)，論環狀排列與珠狀排列，科教圖書
    [2]陳明哲，民國48年(1959)，排列組合，中央書局
    [3]王昌銳，民國61年(1972) ，組合論，百成書局
    [4]王奉民、陳定凱，民國77年(1988)，離散數學導論，儒林書局
    [5]李雲、林文達，民國86年(1997) ，離散數學 ，儒林書局
    [6]張子浩，民國77年(1988) ，整合離散數學，文笙書局
    [7]許振忠，民國86年(1997) ，一些排列組合的演算法，政大應數所
    碩士論文
    Description: 碩士
    國立政治大學
    應用數學研究所
    94751004
    98
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0094751004
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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