RAIRO - Theoretical Informatics and Applications

Research Article

Study of irreducible balanced pairs for substitutive languages

Julien Bernat

IML CNRS UMR 6206 Campus de Luminy, Case 907 13288 Marseille, Cedex 9, France; bernat@iml.univ-mrs.fr


Let $\mathcal{L}$ be a language. A balanced pair (u,v) consists of two words u and v in $\mathcal{L}$ which have the same number of occurrences of each letter. It is irreducible if the pairs of strict prefixes of u and v of the same length do not form balanced pairs. In this article, we are interested in computing the set of irreducible balanced pairs on several cases of languages. We make connections with the balanced pairs algorithm and discrete geometrical constructions related to substitutive languages. We characterize substitutive languages which have infinitely many irreducible balanced pairs of a given form.

(Received January 12 2007)

(Accepted November 23 2007)

(Online publication January 15 2008)

Key Words:

  • Substitutive languages;
  • balanced pairs;
  • algorithm on words.

Mathematics Subject Classification:

  • 68R15