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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/67308


    Title: 有關三元數列的探討
    A study about ternary sequences
    Authors: 林宥廷
    Contributors: 李陽明
    林宥廷
    Keywords: 三元數列
    一對一函數
    ternary sequence
    Date: 2013
    Issue Date: 2014-07-07 11:09:14 (UTC+8)
    Abstract: 長度為n的三元數列(0, 1, 2)，探討(一)0為偶數個1為偶數個，或(二)0為偶數個1為奇數個，或(三)0為奇數個1為偶數個，或(四)0為奇數個1為奇數個的方法數時，就離散的傳統上來說是用遞迴關係去求解。本文將建構一對一函數，利用一對一函數的特性去求此問題的解，與以前的方法比較起來僅需要了解一對一函數的特性即可求解，易懂且不需要用到比較複雜的遞迴觀念。
    The problem of the number of ternary sequences of length n with :
    (a) 0 is even, 1 is even,
    (b) 0 is even, 1 is odd,
    (c) 0 is odd, 1 is even,
    (d) 0 is odd, 1 is odd,
    has been solved by recurrence relations before. We solve the problem by constructingone-to-one functions, and use the characteristics of one-to-one functions to solve this problem. Our method is simpler than those methods which have been done before.
    Reference: (1) Alan Tucker(1994)，Applied Combinatorics(5th edition)，John Wiley & Sons Inc。
    (2) C. L. Liu(2000)，Introduction to Combinatorial Mathematics(International editions 2000)，McGraw-Hill。
    (3) C. L. Liu，Elements of Discrete Mathematics 2nd Edition，McGraw-Hill。
    (4) J.H. van Lint, R.M. Wilson(2001)，A Course in Combinatorics2 edition，Cambridge University Press。
    (5) Jiri Matousek, Jaroslav Nesetril(2008)，Invitation to Discrete Mathematics，Oxford University Press。
    (6) Susanna S. Epp(2003)，Discrete Mathematics with Applications，Cengage Learning。
    (7)張維格(2011)，以雙射函數探討四元數列，國立政治大學應用數學系數學教學碩士在職專班碩士論文。
    (8)奇偶校驗位，維基百科。
    (9)中華民國身分證，維基百科。
    (10)詹承洲、施信毓、吳安宇，低密度奇偶校驗碼的實現與展望，台大系統晶片中心專欄。
    Description: 碩士
    國立政治大學
    應用數學研究所
    97751011
    102
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0097751011
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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