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Substitutive Systems and a Finitary Version of Cobham’s Theorem

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Abstract

We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science Institute of Mathematics, Jagiellonian University, Stanisława Łojasiewicza 6, 30-348, Kraków, Poland

    Jakub Byszewski & Elżbieta Krawczyk

  2. Einstein Institute of Mathematics Edmond J. Safra Campus, The Hebrew University of Jerusalem Givat Ram, Jerusalem, 9190401, Israel

    Jakub Konieczny

Authors
  1. Jakub Byszewski
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  2. Jakub Konieczny
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  3. Elżbieta Krawczyk
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Correspondence to Elżbieta Krawczyk.

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Byszewski, J., Konieczny, J. & Krawczyk, E. Substitutive Systems and a Finitary Version of Cobham’s Theorem. Combinatorica 41, 765–801 (2021). https://doi.org/10.1007/s00493-020-4311-x

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  • DOI: https://doi.org/10.1007/s00493-020-4311-x

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