On a characteristic property of Arnoux–Rauzy sequences

Jacques Justin; Giuseppe Pirillo

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2002)

  • 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 - Informatique Théorique et Applications 36.4 (2002): 385-388. <http://eudml.org/doc/245093>.

@article{Justin2002,
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 - Informatique Théorique et Applications},
keywords = {lexicographic order; Arnoux–Rauzy sequence; episturmian word; sturmian word},
language = {eng},
number = {4},
pages = {385-388},
publisher = {EDP-Sciences},
title = {On a characteristic property of Arnoux–Rauzy sequences},
url = {http://eudml.org/doc/245093},
volume = {36},
year = {2002},
}

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
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/245093
ER -

References

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  1. [1] P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2 n + 1 . Bull. Soc. Math. France 119 (1991) 199-215. Zbl0789.28011MR1116845
  2. [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. Zbl1096.68689MR1466181
  3. [3] J.-P. Borel and F. Laubie, Quelques mots sur la droite projective réelle. J. Théor. Nombres Bordeaux 5 (1993) 123-137. Zbl0839.11008MR1251226
  4. [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. Zbl0981.68126MR1819089
  5. [5] J. Justin, On a paper by Castelli, Mignosi, Restivo. RAIRO: Theoret. Informatics Appl. 34 (2000) 373-377. Zbl0987.68056MR1829233
  6. [6] J. Justin and G. Pirillo, Episturmian words and Episturmian morphisms. Theoret. Comput. Sci. 276 (2002) 281-313. Zbl1002.68116MR1896357
  7. [7] M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press (2002). Zbl1001.68093MR1905123
  8. [8] G. Pirillo, Characterization of infinite Surmian words (in preparation). 
  9. [9] R.N. Risley and L.Q. Zamboni, A generalization of Sturmian sequences, combinatorial structure and transcendence. Acta Arithmetica 95 (2000) 167-184. Zbl0953.11007MR1785413

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