探討雙邊無窮Fibonacci字之性質

Some New Properties about Two-way Infinite Fibonacci Words

于飛 ； 許昭興

《加馬》 39期 (2008/06) Pp. 49-55

https://doi.org/10.30173/JG.200806.0009

摘要

Fibonacci字和Fibonacci字型之性質經過多年之研究，已有很多有趣之結果。本篇論文將特別討論有關雙邊無窮Fibonacci字之有趣性質。

並列摘要

For all χ∈R, define |χ|=n where n∈Z, N≤x＜n+1. For all χ∈R, define [x]=n where n∈Z, Nn-1＜x≤n. Let α=√5-1/2. Define the following two-way infinite binary words:
(a)G=…d(subscript –n)d(subscript –n+1)…d(subscript -1)d0d1…d(subscript n)d(subscript n+1) …, where the nth letter d(subscript n=)「(n+1)α」-「nα」,n∈Z.
(b)H=…e(subscript –n)e(subscript –n+1) …e(subscript -1)e0e1…e(subscript n)e(subscript n+1) …, where the nth letter e(subscript n)=「(n+1)α」-「nα」,n∈Z.
Here, G and H are called two-way infinite Fibonacci words. An infinite word w over {0, 1} is said to be Sturmian if for each n≥1, to has exactly a n+1 factors of length n. A morphism on {0, 1}, is said to be Sturmian if it preserves Sturmian words. In 1999, W.F. Chuan had discussed the action of Sturmian morphisms on α-words (see [5]). In this paper, we determine the action of sturmian morphisms on two-way infinite Fibonacci words.

並列關鍵字

Fibonacci word ； α-words ； Fibonacci word pattern ； Sturmian word ； Sturmian morphism