黃金序列的因子

Factors Of The Golden Sequence

何蕙玲(Hui-Ling Ho)

指導教授 ： 郭蕙芳

中原大學/理學院/應用數學研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400173

摘要

令 a, b 是兩個不同的字母。令 τ = (√5−1)/2。定義無窮字G 第n個字母是a，如果[(n + 1)τ] −[nτ] = 0；第n個字母是 b，如果[(n + 1)τ] −[nτ] = 1，n≧1。G 稱為黃金序列。當m≧0，令Gm表示黃金序列G刪去前m個字母所得到的字尾。在這篇論文中，我們用兩種方法去決定G中每個因子在G中出現的位置。給定兩個不同的正整數m1和m2，我們決定出Gm1和Gm2的最長共同字首及其長度。

關鍵字

因子 ； 黃金序列

並列摘要

Let a, b be two distinct letters. Let τ = (√5−1)/2. Define G to be an infinite word whose nth letter is a (resp., b) if [(n + 1)τ] −[nτ] = 0 (resp., 1). G is called the golden sequence. For m≧0, let Gm denote the suffix of G obtained from G by deleting the first m letters of G. In this thesis, we use two methods to identify the positions where each factor occurs in G. Given two different positive integers m1 and m2, we determine the longest common prefix of Gm1 and Gm2 and its length.

並列關鍵字

factor ； golden sequence

參考文獻

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