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Brun expansions, substitutions and discrete geometry

Thomas Fernique 1 Valerie Berthe 1, *
* Corresponding author
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.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00182696
Contributor : Thomas Fernique <>
Submitted on : Friday, October 26, 2007 - 4:51:14 PM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM
Long-term archiving on: : Monday, April 12, 2010 - 12:49:30 AM

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  • HAL Id : lirmm-00182696, version 1

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Thomas Fernique, Valerie Berthe. Brun expansions, substitutions and discrete geometry. WORDS'07: Sixth International Conference on Words, Sep 2007, Marseille, France. pp.7. ⟨lirmm-00182696⟩

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