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Substitutions par des motifs en dimension 1

Published online by Cambridge University Press:  25 September 2007

N. Pytheas Fogg
N. Pytheas Fogg*
Affiliation:
Institut de mathématiques de Luminy, CNRS UMR 6206 / FRUMAM, case 907, 163 avenue de Luminy, 13288 Marseille Cedex 9, France; pytheas@iml.univ-mrs.fr
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Abstract

Une substitution est un morphisme de monoïdes libres : chaque lettre a pour image un mot, et l'image d'un mot est la concaténation des images de ses lettres. Cet article introduit une généralisation de la notion de substitution, où l'image d'une lettre n'est plus un mot mais un motif, c'est-à-dire un “mot à trous”, l'image d'un mot étant obtenue en raccordant les motifs correspondant à chacune de ses lettres à l'aide de règles locales. On caractérise complètement les substitutions par des motifs qui sont définies sur toute suite biinfinie, et on explique comment les construire. On montre que toute suite biinfinie qui est point fixe d'une substitution par des motifs est substitutive, c'est-à-dire est l'image, par un morphisme lettre à lettre, d'un point fixe de substitution (au sens usuel).

Keywords

Substitutionswordspatternstilings of the lineword combinatoricsSubstitutionsmotsmotifspavages de la droitecombinatoire des mots
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 3 , July 2007 , pp. 267 - 284
Copyright
© EDP Sciences, 2007

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