Selfdual substitutions in dimension one

Authors:
Valérie Berthé;Dirk Frettlöh;Victor Sirvent
Affiliations:
LIAFA - CNRS UMR 7089, Université Paris Diderot-Paris 7, Case 7014, 75205 Paris Cedex 13, France;Institut für Mathematik und Informatik, Universität Greifswald / Institut für Mathematik, FU Berlin, Germany;Departamento de Matemáticas, Universidad Simón Bolívar, Apartado 89000, Caracas 1086-A, Venezuela
Venue:
European Journal of Combinatorics
Year:
2012

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Abstract

There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of two letters/tiles. Furthermore, we obtain necessary and sufficient arithmetic conditions for substitutions being selfdual in this case. Since many connections between the different notions of word/tile substitution are discussed, this paper may also serve as a survey paper on this topic.