Least Periods of Factors of Infinite Words
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Currie, James D.
Currie, James D., and Kalle Saari. "Least Periods of Factors of Infinite Words." RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications 43(1) (2009): 165-178. DOI: 10.1051/ita:2008006.
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 byproduct of our results, we give several new proofs and tightenings of well-known properties of Sturmian words.