Constructing Premaximal Ternary Square-Free Words of Any Level

  • Elena A. Petrova
  • Arseny M. Shur
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


We study extendability of ternary square-free words. Namely, we are interested in the square-free words that cannot be infinitely extended preserving square-freeness. We prove that any positive integer is the length of the longest extension of some ternary square-free word and thus solve an open problem by Allouche and Shallit. We also resolve the two-sided version of this problem.


Factor Order Simple Cycle Acyclic Digraph Word Versus Closed Walk 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Elena A. Petrova
    • 1
  • Arseny M. Shur
    • 1
  1. 1.Ural Federal UniversityEkaterinburgRussia

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