| Issue |
RAIRO-Theor. Inf. Appl.
Volume 43, Number 1, January-March 2009
|
|
|---|---|---|
| Page(s) | 165 - 178 | |
| DOI | https://doi.org/10.1051/ita:2008006 | |
| Published online | 12 March 2008 | |
Least Periods of Factors of Infinite Words
1
Department of Mathematics & Statistics, University of Winnipeg, Winnipeg, R3B2E9, Canada
2
Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland; kasaar@utu.fi
Received:
28
November
2007
Accepted:
6
February
2008
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.
Mathematics Subject Classification: 68R15
Key words: Periodicity / Fibonacci word / Thue-Morse word / Sturmian word.
© EDP Sciences, 2008
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