Displaying similar documents to “An alternative proof that the Fibonacci group F ( 2 , 9 ) is infinite.”

Least Periods of Factors of Infinite Words

James D. Currie, Kalle Saari (2008)

RAIRO - Theoretical Informatics and Applications

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We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci word is the set of Fibonacci numbers. As a by-product of our results, we give several new proofs and tightenings of well-known properties of Sturmian words.

Standard factors of Sturmian words

Gwénaël Richomme, Kalle Saari, Luca Q. Zamboni (2010)

RAIRO - Theoretical Informatics and Applications

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Among the various ways to construct a characteristic Sturmian word, one of the most used consists in defining an infinite sequence of prefixes that are standard. Nevertheless in any characteristic word , some standard words occur that are not prefixes of . We characterize all standard words occurring in any characteristic word (and so in any Sturmian word) using firstly morphisms, then standard prefixes and finally palindromes.

On extremal properties of the Fibonacci word

Julien Cassaigne (2008)

RAIRO - Theoretical Informatics and Applications

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We survey several quantitative problems on infinite words related to repetitions, recurrence, and palindromes, for which the Fibonacci word often exhibits extremal behaviour.