Brun expansions, substitutions and discrete geometry

Thomas Fernique 1 Valerie Berthe 1, *
* Auteur correspondant
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The aim of this lecture is to present a strategy for the problem of discrete plane recognition based on multidimensional continued fractions and S-adic systems. The problem of the discrete plane recognition consists in deciding whether a given set of points with integer coordinates can be described as a plane discretization. The role played respectively by words, substitutions, and classical continued fractions will be played here respectively by stepped surfaces, generalized substitutions and Brun's algorithm. We thus give a geometric interpretation of Brun's continued fraction algorithm in terms of the so-called generalized substitutions introduced by Arnoux and Ito.
Type de document :
Communication dans un congrès
Nicolas Bédaride; Julien Cassaigne. WORDS'07: Sixth International Conference on Words, Sep 2007, Marseille, France. pp.7, 2007, 〈http://iml.univ-mrs.fr/words2007/index.en.html〉
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00182696
Contributeur : Thomas Fernique <>
Soumis le : vendredi 26 octobre 2007 - 16:51:14
Dernière modification le : jeudi 11 janvier 2018 - 06:26:07
Document(s) archivé(s) le : lundi 12 avril 2010 - 00:49:30

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  • HAL Id : lirmm-00182696, version 1

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Thomas Fernique, Valerie Berthe. Brun expansions, substitutions and discrete geometry. Nicolas Bédaride; Julien Cassaigne. WORDS'07: Sixth International Conference on Words, Sep 2007, Marseille, France. pp.7, 2007, 〈http://iml.univ-mrs.fr/words2007/index.en.html〉. 〈lirmm-00182696〉

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