Words Avoiding \(\frac{7}{3}\)-Powers and the Thue–Morse Morphism

  • Narad Rampersad
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3340)


In 1982, Séébold showed that the only overlap-free binary words that are the fixed points of non-identity morphisms are the Thue–Morse word and its complement. We strengthen Séébold’s result by showing that the same result holds if the term ‘overlap-free’ is replaced with ‘\(\frac{7}{3}\)-power-free’. Furthermore, the number \(\frac{7}{3}\) is best possible.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Narad Rampersad
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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