Some Properties of the singular words of the Fibonacci word
Séminaire lotharingien de combinatoire, Tome 30 (1993)
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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
@article{SLC_1993_30_a3,
author = {Wen Zhi-Xiong and Wen Zhi-Ying},
title = {Some {Properties} of the singular words of the {Fibonacci} word},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {30},
year = {1993},
url = {http://geodesic.mathdoc.fr/item/SLC_1993_30_a3/}
}
Wen Zhi-Xiong; Wen Zhi-Ying. Some Properties of the singular words of the Fibonacci word. Séminaire lotharingien de combinatoire, Tome 30 (1993). http://geodesic.mathdoc.fr/item/SLC_1993_30_a3/