Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-23T07:53:25.301Z Has data issue: false hasContentIssue false
  • English
  • Français

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; [email protected].
Luca Q. Zamboni
Affiliation:
Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, TX 76203-1430, USA; [email protected].
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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).