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Functional Stepped Surfaces, Flips and Generalized Substitutions

Pierre Arnoux 1 Valerie Berthe 2 Thomas Fernique 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 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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Pierre Arnoux, Valerie Berthe, Thomas Fernique, Damien Jamet. Functional Stepped Surfaces, Flips and Generalized Substitutions. Theoretical Computer Science, Elsevier, 2007, 380 (3), pp.251-265. ⟨10.1016/j.tcs.2007.03.031⟩. ⟨lirmm-00180395⟩



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