Least Periods of Factors of Infinite Words

James D. Currie; Kalle Saari

RAIRO - Theoretical Informatics and Applications (2008)

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

Abstract

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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.

How to cite

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Currie, James D., and Saari, Kalle. "Least Periods of Factors of Infinite Words." RAIRO - Theoretical Informatics and Applications 43.1 (2008): 165-178. <http://eudml.org/doc/92904>.

@article{Currie2008,
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},
keywords = {Periodicity; Fibonacci word; Thue-Morse word; Sturmian word.; periodicity; Sturmian word},
language = {eng},
month = {3},
number = {1},
pages = {165-178},
publisher = {EDP Sciences},
title = {Least Periods of Factors of Infinite Words},
url = {http://eudml.org/doc/92904},
volume = {43},
year = {2008},
}

TY - JOUR
AU - Currie, James D.
AU - Saari, Kalle
TI - Least Periods of Factors of Infinite Words
JO - RAIRO - Theoretical Informatics and Applications
DA - 2008/3//
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.; periodicity; Sturmian word
UR - http://eudml.org/doc/92904
ER -

References

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  8. N.J. Fine and H.S. Wilf, Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc.16 (1965) 109–114.  Zbl0131.30203
  9. T. Harju and D. Nowotka, Minimal Duval extensions. Int. J. Found. Comput. Sci.15 (2004) 349–354.  Zbl1067.68112
  10. M. Lothaire, Combinatorics on Words. Cambridge University Press, Cambridge (1997).  Zbl0874.20040
  11. M. Lothaire, Algebraic Combinatorics on Words, Encyclopedia of Mathematics and its Applications, Vol. 90. Cambridge University Press, Cambridge (2002).  Zbl1001.68093
  12. F. Mignosi and L.Q. Zamboni, A note on a conjecture of Duval and Sturmian words. RAIRO-Theor. Inf. Appl.36 (2002) 1–3.  Zbl1013.68152
  13. M. Mohammad-Noori and J.D. Currie, Dejean's conjecture and Sturmian words. Eur. J. Combin.28 (2007) 876–890.  Zbl1111.68096
  14. K. Saari, Periods of factors of the Fibonacci word. in Proceedings of the Sixth International Conference on Words (WORDS'07). Institut de Mathématiques de Luminy (2007) 273–279.  

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