Some Properties of the Singular Words of the Fibonacci Word
Some Properties of the Singular Words of the Fibonacci Word
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DOI：
10.1006/eujc.1994.1060
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发表时间：
1994-11
期刊：
影响因子：
--
通讯作者：
Zhi-Xiong Wen;Zhi-Ying Wen
中科院分区：
文献类型：
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作者：
Zhi-Xiong Wen;Zhi-Ying Wen
Fibonacci无穷字的组合性质在数论、分形几何、形式语言、计算复杂性、准晶等数学和物理学中有着重要的意义.本文介绍了Fibonacci无穷字的奇异字，并讨论了它们的性质.我们建立了两个分解的斐波那契字在单数的话和他们的后果。利用这些结果，我们讨论了Fibonacci字的局部同构和因子的重叠性质。此外，我们还对有关特殊词的结果和因子的幂给出了新的证明。
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.