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A Note on a Conjecture of Duval and Sturmian Words

Published online by Cambridge University Press:  15 December 2002

Filippo Mignosi  and
Luca Q. Zamboni
Filippo Mignosi
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi di Palermo, Via Archirafi 34, 90123 Palermo, Italia; mignosi@dipmat.math.unipa.it.
Luca Q. Zamboni
Affiliation:
Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, TX 76203-1430, USA; luca@unt.edu.
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Abstract

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

Keywords

Bordered wordsSturmian words.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 1 , January 2002 , pp. 1 - 3
Copyright
© EDP Sciences, 2002

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References

P. Arnoux and G. Rauzy, Représentation géométrique des suites de complexité 2n+1.Bull. Soc. Math. France 119 (1991) 199-215.
Assous, R. and Pouzet, M., Une Caractérisation des mots périodiques. Discrete Math. 25 (1979) 1-5. CrossRef
Duval, J.P., Relationship between the Period of a Finite Word and the Length of its Unbordered Segments. Discrete Math. 40 (1982) 31-44. CrossRef
Ehrenfeucht, A. and Silberger, D.M., Periodicity and Unbordered Segments of words. Discrete Math. 26 (1979) 101-109. CrossRef
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
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).
Mignosi, F. and Séébold, P., Morphismes sturmiens et règles de Rauzy. J. Théorie des Nombres de Bordeaux 5 (1993) 221-233. CrossRef
Rauzy, G., 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.
R. Risley and L.Q. Zamboni, A generalization of Sturmian sequences; combinatorial structure and transcendence. Acta Arith. 95 (2000).