Functional stepped surfaces, flips, and generalized substitutions
Identifieur interne : 004E88 ( Main/Merge ); précédent : 004E87; suivant : 004E89Functional stepped surfaces, flips, and generalized substitutions
Auteurs : Pierre Arnoux [France] ; Valérie Berthe [France] ; Thomas Fernique [France] ; Damien Jamet [France]Source :
- Theoretical computer science [ 0304-3975 ] ; 2007.
Descripteurs français
- Pascal (Inist)
- Wicri :
- topic : Plan.
English descriptors
- KwdEn :
Abstract
A substitution is a non-erasing morphism of the free monoid. The notion of multidimensional substitution of non-constant length acting on multidimensional words is proved to be well-defined on the set of two-dimensional words related to discrete approximations of irrational planes. Such a multidimensional substitution can be associated with any usual unimodular substitution. The aim of this paper is to extend the domain of definition of such multidimensional substitutions to functional stepped surfaces. One central tool for this extension is the notion of flips acting on tilings by lozenges of the plane.
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Pascal:08-0194372Le document en format XML
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<term>Discrete scheme</term>
<term>Free monoid</term>
<term>Functional</term>
<term>Morphism</term>
<term>Plane</term>
<term>Substitution</term>
<term>Surface</term>
<term>Tiling</term>
<term>Two-dimensional calculations</term>
<term>Word combinatorics</term>
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<term>Surface</term>
<term>Substitution</term>
<term>Morphisme</term>
<term>Monoïde libre</term>
<term>Calcul 2 dimensions</term>
<term>Schéma discret</term>
<term>Approximation</term>
<term>Plan</term>
<term>Définition</term>
<term>Pavage</term>
<term>Géométrie discrète</term>
<term>Combinatoire mot</term>
<term>Informatique théorique</term>
<term>Mot sturmien</term>
<term>05B45</term>
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<front><div type="abstract" xml:lang="en">A substitution is a non-erasing morphism of the free monoid. The notion of multidimensional substitution of non-constant length acting on multidimensional words is proved to be well-defined on the set of two-dimensional words related to discrete approximations of irrational planes. Such a multidimensional substitution can be associated with any usual unimodular substitution. The aim of this paper is to extend the domain of definition of such multidimensional substitutions to functional stepped surfaces. One central tool for this extension is the notion of flips acting on tilings by lozenges of the plane.</div>
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