# Least periods of factors of infinite words

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2009)

- Volume: 43, Issue: 1, page 165-178
- ISSN: 0988-3754

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topCurrie, James D., and Saari, Kalle. "Least periods of factors of infinite words." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 43.1 (2009): 165-178. <http://eudml.org/doc/245812>.

@article{Currie2009,

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.},

author = {Currie, James D., Saari, Kalle},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {periodicity; Fibonacci word; Thue-Morse word; sturmian word; Sturmian word},

language = {eng},

number = {1},

pages = {165-178},

publisher = {EDP-Sciences},

title = {Least periods of factors of infinite words},

url = {http://eudml.org/doc/245812},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Currie, James D.

AU - Saari, Kalle

TI - Least periods of factors of infinite words

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2009

PB - EDP-Sciences

VL - 43

IS - 1

SP - 165

EP - 178

AB - 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.

LA - eng

KW - periodicity; Fibonacci word; Thue-Morse word; sturmian word; Sturmian word

UR - http://eudml.org/doc/245812

ER -

## References

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- [10] M. Lothaire, Combinatorics on Words. Cambridge University Press, Cambridge (1997). Zbl0874.20040MR1475463
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