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Least Periods of Factors of Infinite Words

Published online by Cambridge University Press:  12 March 2008

James D. Currie  and
Kalle Saari
James D. Currie
Affiliation:
Department of Mathematics & Statistics, University of Winnipeg, Winnipeg, R3B2E9, Canada
Kalle Saari
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland; kasaar@utu.fi
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Abstract

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.

Keywords

PeriodicityFibonacci wordThue-Morse wordSturmian word.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 1 , January 2009 , pp. 165 - 178
Copyright
© EDP Sciences, 2008

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