有關三元數列的探討

• Main Author: 林宥廷
• Language: 中文
• Published: 國立政治大學
• Subjects: 三元數列; 一對一函數; ternary sequence
• Online Access: http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22G0097751011%22.

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.