On Highly Repetitive and Power Free Words

  • Narad Rampersad
  • Elise Vaslet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)


Answering a question of Richomme, Currie and Rampersad proved that 7/3 is the infimum of the real numbers α > 2 such that there exists an infinite binary word that avoids α-powers but is highly 2-repetitive, i.e., contains arbitrarily large squares beginning at every position. In this paper, we prove similar statements about β-repetitive words, for some other β’s, on the binary and the ternary alphabets.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Narad Rampersad
    • 1
  • Elise Vaslet
    • 2
  1. 1.Department of MathematicsUniversity of LiégeBelgium
  2. 2.Institut de Mathématiques de LuminyUniversité Aix-Marseille IIFrance

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