RAIRO - Theoretical Informatics and Applications

Research Article

On a characteristic property of ARNOUX–RAUZY sequences

Jacques Justina1 and Giuseppe Pirilloa2

a1 LIAFA, Université Paris VII, Case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France; justin@liafa.jussieu.fr.

a2 IAMI, NCR, Viale Morgagni 67/a, 50134 Firenze, Italy; pirillo@udini.math.unifi.it.


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

(Received April 2002)

(Accepted November 2002)

(Online publication February 15 2003)

Key Words:

  • Lexicographic order;
  • Arnoux–Rauzy sequence;
  • Episturmian word;
  • Sturmian word

Mathematics Subject Classification:

  • 68R15