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Least periods of factors of infinite words

James D. Currie;  Kalle Saari — 2009

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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.

Least Periods of Factors of Infinite Words

James D. Currie;  Kalle Saari — 2008

RAIRO - Theoretical Informatics and Applications

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.

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