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On a characteristic property of ARNOUX–RAUZY sequences

Published online by Cambridge University Press:  15 February 2003

Jacques Justin  and
Giuseppe Pirillo
Jacques Justin
Affiliation:
LIAFA, Université Paris VII, Case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France; justin@liafa.jussieu.fr.
Giuseppe Pirillo
Affiliation:
IAMI, NCR, Viale Morgagni 67/a, 50134 Firenze, Italy; pirillo@udini.math.unifi.it.
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Abstract

Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet.

Keywords

Lexicographic orderArnoux–Rauzy sequenceEpisturmian wordSturmian word
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 4 , October 2002 , pp. 385 - 388
Copyright
© EDP Sciences, 2002

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References

Arnoux, P. and Rauzy, G., Représentation géométrique de suites de complexité 2n+1. Bull. Soc. Math. France 119 (1991) 199-215. CrossRef
J. Berstel, Recent results in Sturmian words, in Developments in Language Theory II, edited by J. Dassow, G. Rozenbergand A. Salomaa. World Scientific (1996) 13-24.
Borel, J.-P. and Laubie, F., Quelques mots sur la droite projective réelle. J. Théor. Nombres Bordeaux 5 (1993) 123-137.
Droubay, X., Justin, J. and Pirillo, G., Episturmian words and some constructions of de Luca and Rauzy. Theoret. Comput. Sci. 255 (2001) 539-553. CrossRef
Justin, J., On a paper by Castelli, Mignosi, Restivo. RAIRO: Theoret. Informatics Appl. 34 (2000) 373-377.
Justin, J. and Pirillo, G., Episturmian words and Episturmian morphisms. Theoret. Comput. Sci. 276 (2002) 281-313. CrossRef
M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press (2002).
G. Pirillo, Characterization of infinite Surmian words (in preparation).
Risley, R.N. and Zamboni, L.Q., A generalization of Sturmian sequences, combinatorial structure and transcendence. Acta Arithmetica 95 (2000) 167-184.