Brun expansions, substitutions and discrete geometry - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
Conference Papers Year : 2007

Brun expansions, substitutions and discrete geometry

Thomas Fernique
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Valerie Berthe
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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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Dates and versions

lirmm-00182696 , version 1 (26-10-2007)

Identifiers

  • HAL Id : lirmm-00182696 , version 1

Cite

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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