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Generalized Substitutions and Stepped Surfaces

Pierre Arnoux 1 Valerie Berthe 2 Damien Jamet 3
2 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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 introduced in [AI01,ABS04] is proved to be sell-defined on the set of two-dimensional words related to discrete approximations of irrational planes. Such a multidimensional substitution can be associated to any usual Pisot unimodular substitution. The aim of this paper is to try to extend the domain of definition of such multidimensional substitutions. In particular, we study an example of a multidimensional substitution which acts on a stepped surface in the sense of [Jam04,JP04].
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Conference papers
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https://hal.archives-ouvertes.fr/hal-00580567
Contributor : Damien Jamet <>
Submitted on : Tuesday, March 29, 2011 - 10:56:47 AM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM
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  • HAL Id : hal-00580567, version 1

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Pierre Arnoux, Valerie Berthe, Damien Jamet. Generalized Substitutions and Stepped Surfaces. 5-th International Conference on Words, Sep 2005, Montreal, Canada. ⟨hal-00580567⟩

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