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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)

Abstract

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.

Keywords

Factor Order Simple Cycle Acyclic Digraph Word Versus Closed Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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