On a characteristic property of ARNOUX–RAUZY sequences

Jacques Justin; Giuseppe Pirillo

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 36, Issue: 4, page 385-388
  • ISSN: 0988-3754

Abstract

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

How to cite

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Justin, Jacques, and Pirillo, Giuseppe. "On a characteristic property of ARNOUX–RAUZY sequences." RAIRO - Theoretical Informatics and Applications 36.4 (2010): 385-388. <http://eudml.org/doc/92708>.

@article{Justin2010,
abstract = { Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet. },
author = {Justin, Jacques, Pirillo, Giuseppe},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Lexicographic order; Arnoux–Rauzy sequence; Episturmian word; Sturmian word},
language = {eng},
month = {3},
number = {4},
pages = {385-388},
publisher = {EDP Sciences},
title = {On a characteristic property of ARNOUX–RAUZY sequences},
url = {http://eudml.org/doc/92708},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Justin, Jacques
AU - Pirillo, Giuseppe
TI - On a characteristic property of ARNOUX–RAUZY sequences
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 4
SP - 385
EP - 388
AB - Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet.
LA - eng
KW - Lexicographic order; Arnoux–Rauzy sequence; Episturmian word; Sturmian word
UR - http://eudml.org/doc/92708
ER -

References

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  1. P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2n+1. Bull. Soc. Math. France119 (1991) 199-215.  
  2. 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.  
  3. J.-P. Borel and F. Laubie, Quelques mots sur la droite projective réelle. J. Théor. Nombres Bordeaux5 (1993) 123-137.  
  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.  
  5. J. Justin, On a paper by Castelli, Mignosi, Restivo. RAIRO: Theoret. Informatics Appl.34 (2000) 373-377.  
  6. J. Justin and G. Pirillo, Episturmian words and Episturmian morphisms. Theoret. Comput. Sci.276 (2002) 281-313.  
  7. M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press (2002).  
  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 Arithmetica95 (2000) 167-184.  

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