Finiteness properties for Pisot $S$-adic tilings

Pierre Arnoux 1 Valerie Berthe 2 Anne Siegel 3
2 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 SYMBIOSE - Biological systems and models, bioinformatics and sequences
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : In this paper, we will first formulate and prove some equivalent sufficient conditions to obtain the tiling property for a Pisot unimodular substitution. We will then apply these condition to the more general framework of adic systems, to extend to this more general (and non algebraic) case results already known for the substitutive case.
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https://hal.inria.fr/inria-00180242
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Pierre Arnoux, Valerie Berthe, Anne Siegel. Finiteness properties for Pisot $S$-adic tilings. Journées Montoises d'Informatique Théorique, Aug 2006, RENNES, France. ⟨inria-00180242⟩

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