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Multidimensional Sturmian Sequences and Generalized Substitutions

Thomas Fernique 1
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : This paper is devoted to a study on the way \emph{generalized substitutions} - a multi-dimensional extension of substitutions - act on \emph{multi-dimensional Sturmian sequences}. We give a sufficient condition under which these multi-dimensional Sturmian sequences are obtained by iterated compositions of generalized substitutions. This condition relies on Brun expansions - a multi-dimensional extension of continued fraction expansions.
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Contributor : Thomas Fernique <>
Submitted on : Friday, May 25, 2007 - 1:38:47 PM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM
Long-term archiving on: : Thursday, April 8, 2010 - 5:53:06 PM


  • HAL Id : lirmm-00149363, version 1



Thomas Fernique. Multidimensional Sturmian Sequences and Generalized Substitutions. International Journal of Foundations of Computer Science, World Scientific Publishing, 2006, 17, pp.575-600. ⟨lirmm-00149363⟩



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