A Set of Sequences of Complexity \(2n+1\)

  • J. Cassaigne
  • S. LabbéEmail author
  • J. Leroy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10432)


We prove the existence of a ternary sequence of factor complexity \(2n+1\) for any given vector of rationally independent letter frequencies. Such sequences are constructed from an infinite product of two substitutions according to a particular Multidimensional Continued Fraction algorithm. We show that this algorithm is conjugate to a well-known one, the Selmer algorithm. Experimentations (Baldwin, 1992) suggest that their second Lyapunov exponent is negative which presages finite balance properties.


Substitutions Factor complexity Selmer Continued fraction Bispecial 



We are thankful to Valérie Berthé for her enthusiasm toward this project and for the referees for their thorough reading and pertinent suggestions.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut de mathématiques de Marseille, CNRS UMR 7373Marseille Cedex 09France
  2. 2.CNRS, LaBRI, UMR 5800TalenceFrance
  3. 3.Institut de mathématique, Université de LiègeLiègeBelgium

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