On a paper by Castelli, Mignosi, Restivo

Jacques Justin

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 34, Issue: 5, page 373-377
  • ISSN: 0988-3754

Abstract

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Fine and Wilf's theorem has recently been extended to words having three periods. Following the method of the authors we extend it to an arbitrary number of periods and deduce from that a characterization of generalized Arnoux-Rauzy sequences or episturmian infinite words.

How to cite

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Justin, Jacques. "On a paper by Castelli, Mignosi, Restivo." RAIRO - Theoretical Informatics and Applications 34.5 (2010): 373-377. <http://eudml.org/doc/222008>.

@article{Justin2010,
abstract = { Fine and Wilf's theorem has recently been extended to words having three periods. Following the method of the authors we extend it to an arbitrary number of periods and deduce from that a characterization of generalized Arnoux-Rauzy sequences or episturmian infinite words. },
author = {Justin, Jacques},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Fine and Wilf theorem; Arnoux-Rauzy sequence; episturmian word.; Arnoux-Rauzy sequences; episturmian infinite words},
language = {eng},
month = {3},
number = {5},
pages = {373-377},
publisher = {EDP Sciences},
title = {On a paper by Castelli, Mignosi, Restivo},
url = {http://eudml.org/doc/222008},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Justin, Jacques
TI - On a paper by Castelli, Mignosi, Restivo
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 5
SP - 373
EP - 377
AB - Fine and Wilf's theorem has recently been extended to words having three periods. Following the method of the authors we extend it to an arbitrary number of periods and deduce from that a characterization of generalized Arnoux-Rauzy sequences or episturmian infinite words.
LA - eng
KW - Fine and Wilf theorem; Arnoux-Rauzy sequence; episturmian word.; Arnoux-Rauzy sequences; episturmian infinite words
UR - http://eudml.org/doc/222008
ER -

References

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  1. P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2n+1. Bull. Soc. Math. France119 (1991) 199-215.  
  2. M.G. Castelli, F. Mignosi and A. Restivo, Fine and Wilf's theorem for three periods and a generalization of Sturmian words. Theoret. Comput. Sci.218 (1999) 83-94.  
  3. A. de Luca, Sturmian words, structure, combinatorics and their arithmetics. Theoret. Comput. Sci.183 (1997) 45-82.  
  4. X. Droubay, J. Justin and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy. Theoret. Comput. Sci. (to appear).  
  5. N.J. Fine and H.S. Wilf, Uniqueness Theorem for Periodic Functions. Proc. Am. Math. Soc.16 (1965) 109-114.  
  6. J. Justin and G. Pirillo, Episturmian words and episturmian morphisms. Preprint.  
  7. M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA (1983).  

Citations in EuDML Documents

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  1. Francine Blanchet-Sadri, Sean Simmons, Amelia Tebbe, Amy Veprauskas, Abelian periods, partial words, and an extension of a theorem of Fine and Wilf
  2. Štěpán Holub, On multiperiodic words
  3. Gwenael Richomme, Some algorithms to compute the conjugates of episturmian morphisms
  4. Jacques Justin, Giuseppe Pirillo, On a characteristic property of Arnoux–Rauzy sequences
  5. Jacques Justin, Giuseppe Pirillo, On a characteristic property of ARNOUX–RAUZY sequences
  6. Gwenael Richomme, Some algorithms to compute the conjugates of Episturmian morphisms
  7. Jacques Justin, Episturmian morphisms and a Galois theorem on continued fractions
  8. Jacques Justin, Episturmian morphisms and a Galois theorem on continued fractions
  9. Amy Glen, Jacques Justin, Episturmian words: a survey

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