✦ LIBER ✦

Some Properties of the Singular Words of the Fibonacci Word

✍ Scribed by Wen Zhi-Xiong; Wen Zhi-Ying

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 324 KB
Volume: 15
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1994.1060

No coin nor oath required. For personal study only.

✦ Synopsis

The combinatorial properties of the Fibonacci infinite word are of great interest in some aspects of mathematics and physics, such as number theory, fractal geometry, formal language, computational complexity, quasicrystals etc.

In this note, we introduce the singular words of the Fibonacci infinite word and discuss their properties. We establish two decompositions of the Fibonacci word in singular words and their consequences. By using these results, we discuss the local isomorphism of the Fibonacci word and the overlap properties of the factors. Moreover, we also give new proofs for the results on special words and the power of the factors.

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