A note on a conjecture of Duval and sturmian words

Filippo Mignosi; Luca Q. Zamboni

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2002)

  • 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 - Informatique Théorique et Applications 36.1 (2002): 1-3. <http://eudml.org/doc/245344>.

@article{Mignosi2002,
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 - Informatique Théorique et Applications},
keywords = {bordered words; sturmian words; Sturmian words},
language = {eng},
number = {1},
pages = {1-3},
publisher = {EDP-Sciences},
title = {A note on a conjecture of Duval and sturmian words},
url = {http://eudml.org/doc/245344},
volume = {36},
year = {2002},
}

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 - Informatique Théorique et Applications
PY - 2002
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/245344
ER -

References

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  1. [1] P. Arnoux and G. Rauzy, Représentation géométrique des suites de complexité 2 n + 1 . Bull. Soc. Math. France 119 (1991) 199-215. Zbl0789.28011MR1116845
  2. [2] R. Assous and M. Pouzet, Une Caractérisation des mots périodiques. Discrete Math. 25 (1979) 1-5. Zbl0407.68087MR522741
  3. [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. Zbl0475.68038MR676710
  4. [4] A. Ehrenfeucht and D.M. Silberger, Periodicity and Unbordered Segments of words. Discrete Math. 26 (1979) 101-109. Zbl0416.20051MR535237
  5. [5] Lothaire, Algebraic Combinatorics on Words, Chap. 9 Periodicity, Chap. 3 Sturmian Words. Cambridge University Press (to appear). Available at http://www-igm.univ-mlv.fr/berstel Zbl1001.68093MR1905123
  6. [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). Zbl0966.68167MR1854493
  7. [7] F. Mignosi and P. Séébold, Morphismes sturmiens et règles de Rauzy. J. Théorie des Nombres de Bordeaux 5 (1993) 221-233. Zbl0797.11029MR1265903
  8. [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. Zbl0613.10044MR814741
  9. [9] R. Risley and L.Q. Zamboni, A generalization of Sturmian sequences; combinatorial structure and transcendence. Acta Arith. 95 (2000). Zbl0953.11007MR1785413

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