A Note on a Conjecture of Duval and Sturmian Words

Filippo Mignosi; Luca Q. Zamboni

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 36, Issue: 1, page 1-3
  • ISSN: 0988-3754

Abstract

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We prove a long standing conjecture of Duval in the special case of Sturmian words.

How to cite

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Mignosi, Filippo, and Zamboni, Luca Q.. "A Note on a Conjecture of Duval and Sturmian Words." RAIRO - Theoretical Informatics and Applications 36.1 (2010): 1-3. <http://eudml.org/doc/92688>.

@article{Mignosi2010,
abstract = { We prove a long standing conjecture of Duval in the special case of Sturmian words. },
author = {Mignosi, Filippo, Zamboni, Luca Q.},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Bordered words; Sturmian words.; Sturmian words},
language = {eng},
month = {3},
number = {1},
pages = {1-3},
publisher = {EDP Sciences},
title = {A Note on a Conjecture of Duval and Sturmian Words},
url = {http://eudml.org/doc/92688},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Mignosi, Filippo
AU - Zamboni, Luca Q.
TI - A Note on a Conjecture of Duval and Sturmian Words
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 1
SP - 1
EP - 3
AB - We prove a long standing conjecture of Duval in the special case of Sturmian words.
LA - eng
KW - Bordered words; Sturmian words.; Sturmian words
UR - http://eudml.org/doc/92688
ER -

References

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  1. P. Arnoux and G. Rauzy, Représentation géométrique des suites de complexité 2n+1.Bull. Soc. Math. France119 (1991) 199-215.  Zbl0789.28011
  2. R. Assous and M. Pouzet, Une Caractérisation des mots périodiques. Discrete Math.25 (1979) 1-5.  Zbl0407.68087
  3. J.P. Duval, Relationship between the Period of a Finite Word and the Length of its Unbordered Segments. Discrete Math.40 (1982) 31-44.  Zbl0475.68038
  4. A. Ehrenfeucht and D.M. Silberger, Periodicity and Unbordered Segments of words. Discrete Math.26 (1979) 101-109.  Zbl0416.20051
  5. Lothaire, Algebraic Combinatorics on Words, Chap. 9 Periodicity, Chap. 3 Sturmian Words. Cambridge University Press (to appear). Available at  Zbl1001.68093URIhttp://www-igm.univ-mlv.fr/berstel
  6. G. Pirillo, A rather curious characteristic property of standard Sturmian words, to appear in Algebraic Combinatorics, edited by G. Rota, D. Senato and H. Crapo. Springer-Verlag Italia, Milano (in press).  Zbl0966.68167
  7. F. Mignosi and P. Séébold, Morphismes sturmiens et règles de Rauzy. J. Théorie des Nombres de Bordeaux5 (1993) 221-233.  
  8. G. Rauzy, Mots infinis en arithmétique, in Automata on Infinite Words, edited by M. Nivat and D. Perrin. Lecture Notes in Comput. Sci.192 (1985) 167-171.  Zbl0613.10044
  9. R. Risley and L.Q. Zamboni, A generalization of Sturmian sequences; combinatorial structure and transcendence. Acta Arith.95 (2000).  Zbl0953.11007

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