On a characteristic property of Arnoux-Rauzy sequences
Justin, Jacques ; Pirillo, Giuseppe
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002), p. 385-388 / Harvested from Numdam
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Here we give a characterization of Arnoux-Rauzy sequences by the way of the lexicographic orderings of their alphabet.

Publié le : 2002-01-01
DOI : https://doi.org/10.1051/ita:2003005
Classification:  68R15 
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     author = {Justin, Jacques and Pirillo, Giuseppe},
     title = {On a characteristic property of Arnoux-Rauzy sequences},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {36},
     year = {2002},
     pages = {385-388},
     doi = {10.1051/ita:2003005},
     zbl = {1060.68094},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2002__36_4_385_0}
}

Justin, Jacques; Pirillo, Giuseppe. On a characteristic property of Arnoux-Rauzy sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) pp. 385-388. doi : 10.1051/ita:2003005. http://gdmltest.u-ga.fr/item/ITA_2002__36_4_385_0/

[1] P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2n+1. Bull. Soc. Math. France 119 (1991) 199-215. | Numdam | MR 1116845 | Zbl 0789.28011

[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 1466181 | Zbl 1096.68689

[3] J.-P. Borel and F. Laubie, Quelques mots sur la droite projective réelle. J. Théor. Nombres Bordeaux 5 (1993) 123-137. | Numdam | MR 1251226 | Zbl 0839.11008

[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 1819089 | Zbl 0981.68126

[5] J. Justin, On a paper by Castelli, Mignosi, Restivo. RAIRO: Theoret. Informatics Appl. 34 (2000) 373-377. | Numdam | MR 1829233 | Zbl 0987.68056

[6] J. Justin and G. Pirillo, Episturmian words and Episturmian morphisms. Theoret. Comput. Sci. 276 (2002) 281-313. | MR 1896357 | Zbl 1002.68116

[7] M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press (2002). | MR 1905123 | Zbl 1001.68093

[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 1785413 | Zbl 0953.11007