#####
Séminaire Lotharingien de Combinatoire, B30d (1993), 14
pp.

[Formerly: Publ. I.R.M.A. Strasbourg, 1993, 1993/034, p.
115-128]

# Wen Zhi-Xiong, Wen Zhi-Ying

#
Some Properties of the singular words of the Fibonacci word

**Abstract.**
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.

Wen Zhi-Xiong, Department of Physics, Wuhan University, China
Wen Zhi-Ying, Department of Mathematics, Wuhan University, China

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