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 
@article{ITA_2002__36_4_385_0,
     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},
     pages = {385--388},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     doi = {10.1051/ita:2003005},
     zbl = {1060.68094},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita:2003005/}
}
TY  - JOUR
AU  - Justin, Jacques
AU  - Pirillo, Giuseppe
TI  - On a characteristic property of Arnoux-Rauzy sequences
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2002
SP  - 385
EP  - 388
VL  - 36
IS  - 4
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/ita:2003005/
DO  - 10.1051/ita:2003005
LA  - en
ID  - ITA_2002__36_4_385_0
ER  - 
%0 Journal Article
%A Justin, Jacques
%A Pirillo, Giuseppe
%T On a characteristic property of Arnoux-Rauzy sequences
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2002
%P 385-388
%V 36
%N 4
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/ita:2003005/
%R 10.1051/ita:2003005
%G en
%F 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) no. 4, pp. 385-388. doi : 10.1051/ita:2003005. https://www.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

  • Ghareghani, N.; Mohammad-Noori, M.; Sharifani, P. On z-factorization and c-factorization of standard episturmian words, Theoretical Computer Science, Volume 412 (2011) no. 39, p. 5232 | DOI:10.1016/j.tcs.2011.05.035
  • Glen, Amy; Levé, Florence; Richomme, Gwénaël Directive words of episturmian words: equivalences and normalization, RAIRO - Theoretical Informatics and Applications, Volume 43 (2009) no. 2, p. 299 | DOI:10.1051/ita:2008029
  • Glen, Amy; Justin, Jacques Episturmian words: a survey, RAIRO - Theoretical Informatics and Applications, Volume 43 (2009) no. 3, p. 403 | DOI:10.1051/ita/2009003
  • Glen, Amy; Justin, Jacques; Pirillo, Giuseppe Characterizations of finite and infinite episturmian words via lexicographic orderings, European Journal of Combinatorics, Volume 29 (2008) no. 1, p. 45 | DOI:10.1016/j.ejc.2007.01.002
  • Bernat, Julien Study of irreducible balanced pairs for substitutive languages, RAIRO - Theoretical Informatics and Applications, Volume 42 (2008) no. 4, p. 663 | DOI:10.1051/ita:2007062
  • Glen, Amy A characterization of fine words over a finite alphabet, Theoretical Computer Science, Volume 391 (2008) no. 1-2, p. 51 | DOI:10.1016/j.tcs.2007.10.029
  • Glen, Amy; Levé, Florence; Richomme, Gwénaël Quasiperiodic and Lyndon episturmian words, Theoretical Computer Science, Volume 409 (2008) no. 3, p. 578 | DOI:10.1016/j.tcs.2008.09.056
  • Berstel, Jean Sturmian and Episturmian Words, Algebraic Informatics, Volume 4728 (2007), p. 23 | DOI:10.1007/978-3-540-75414-5_2
  • Glen, Amy Powers in a class of A-strict standard episturmian words, Theoretical Computer Science, Volume 380 (2007) no. 3, p. 330 | DOI:10.1016/j.tcs.2007.03.023
  • Richomme, G. Conjugacy of morphisms and Lyndon decomposition of standard Sturmian words, Theoretical Computer Science, Volume 380 (2007) no. 3, p. 393 | DOI:10.1016/j.tcs.2007.03.028
  • Pirillo, Giuseppe Inequalities characterizing standard Sturmian and episturmian words, Theoretical Computer Science, Volume 341 (2005) no. 1-3, p. 276 | DOI:10.1016/j.tcs.2005.04.008
  • Jenkinson, Oliver; Zamboni, Luca Q. Characterisations of balanced words via orderings, Theoretical Computer Science, Volume 310 (2004) no. 1-3, p. 247 | DOI:10.1016/s0304-3975(03)00397-9

Cité par 12 documents. Sources : Crossref