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

Brun expansions, substitutions and discrete geometry

Thomas Fernique
  • Function : Author
  • PersonId : 938430
Valerie Berthe
Connectez-vous pour contacter l'auteur


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.
Fichier principal
Vignette du fichier
Berthe-Fernique.pdf (239.28 Ko) Télécharger le fichier

Dates and versions

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


  • HAL Id : lirmm-00182696 , version 1


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⟩
72 View
232 Download


Gmail Facebook X LinkedIn More