On the Tree of Binary Cube-Free Words

  • Elena A. Petrova
  • Arseny M. ShurEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10396)


We present two related results on the prefix tree of all binary cube-free words. First, we show that non-branching paths in this tree are short: such a path from a node of nth level has length \(O(\log n)\). Second, we prove that the lower density of the set of branching points along any infinite path is at least 23/78. Our results are based on a technical theorem describing the mutual location of “almost cubes” in a cube-free word.


Cube-free word Power-free word Prefix tree 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Natural Sciences and MathematicsUral Federal UniversityEkaterinburgRussia

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