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Generating discrete planes with substitutions

By Valerie Berthe, Jérémie Bourdon, Timo Jolivet and Anne Siegel

Abstract

International audienceGiven a finite set S of unimodular Pisot substitutions, we provide a method for characterizing the infinite sequences over S that allow to generate a full discrete plane when, starting from a finite seed, we iterate the multidimensional dual substitutions associated with S. We apply our results to study the substitutions associated with the Brun multidimensional continued fraction algorithm

Topics: [ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM]
Publisher: HAL CCSD
Year: 2013
OAI identifier: oai:HAL:hal-00853758v1
Provided by: Hal-Diderot
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