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Study of irreducible balanced pairs for substitutive languages

Published online by Cambridge University Press:  15 January 2008

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

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.

Keywords

Substitutive languagesbalanced pairsalgorithm on words.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 4: Fibonacci words , October 2008 , pp. 663 - 678
Copyright
© EDP Sciences, 2008

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