On a characteristic property of Arnoux-Rauzy sequences
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 385-388.

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

DOI : 10.1051/ita:2003005
Classification : 68R15
Mots-clés : lexicographic order, Arnoux-Rauzy sequence, episturmian word, sturmian word 
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     title = {On a characteristic property of {Arnoux-Rauzy} sequences},
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Justin, Jacques; Pirillo, Giuseppe. On a characteristic property of Arnoux-Rauzy sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 385-388. doi : 10.1051/ita:2003005. http://archive.numdam.org/articles/10.1051/ita:2003005/

[1] P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2n+1. Bull. Soc. Math. France 119 (1991) 199-215. | Numdam | MR | Zbl

[2] J. Berstel, Recent results in Sturmian words, in Developments in Language Theory II, edited by J. Dassow, G. Rozenberg&A. Salomaa. World Scientific (1996) 13-24. | MR | Zbl

[3] J.-P. Borel and F. Laubie, Quelques mots sur la droite projective réelle. J. Théor. Nombres Bordeaux 5 (1993) 123-137. | Numdam | MR | Zbl

[4] X. Droubay, J. Justin and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy. Theoret. Comput. Sci. 255 (2001) 539-553. | MR | Zbl

[5] J. Justin, On a paper by Castelli, Mignosi, Restivo. RAIRO: Theoret. Informatics Appl. 34 (2000) 373-377. | Numdam | MR | Zbl

[6] J. Justin and G. Pirillo, Episturmian words and Episturmian morphisms. Theoret. Comput. Sci. 276 (2002) 281-313. | MR | Zbl

[7] M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press (2002). | MR | Zbl

[8] G. Pirillo, Characterization of infinite Surmian words (in preparation).

[9] R.N. Risley and L.Q. Zamboni, A generalization of Sturmian sequences, combinatorial structure and transcendence. Acta Arithmetica 95 (2000) 167-184. | MR | Zbl

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