Balancedness of Arnoux-Rauzy and Brun Words

  • Vincent Delecroix
  • Tomáš Hejda
  • Wolfgang Steiner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8079)


We study balancedness properties of words given by the Arnoux-Rauzy and Brun multi-dimensional continued fraction algorithms. We show that almost all Brun words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely balanced; in particular, boundedness of the strong partial quotients implies balancedness. On the other hand, we provide examples of unbalanced Brun words on 3 letters.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vincent Delecroix
    • 1
  • Tomáš Hejda
    • 2
    • 3
  • Wolfgang Steiner
    • 3
  1. 1.Institut de Mathématiques de Jussieu, CNRS UMR 7586Université Paris Diderot – Paris 7Paris Cedex 13France
  2. 2.Department of Mathematics and Doppler Institute, FNSPECzech Technical University in PragueCzech Republic
  3. 3.LIAFA, CNRS UMR 7089Université Paris Diderot – Paris 7Paris Cedex 13France

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