An Answer to a Conjecture on Overlaps in Partial Words Using Periodicity Algorithms

  • Francine Blanchet-Sadri
  • Robert Mercaş
  • Abraham Rashin
  • Elara Willett
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)


We propose an algorithm that given as input a full word w of length n, and positive integers p and d, outputs (if any exists) a maximal p-periodic partial word contained in w with the property that no two holes are within distance d. Our algorithm runs in O(nd) time and is used for the study of freeness of partial words. Furthermore, we construct an infinite word over a five-letter alphabet that is overlap-free even after the insertion of an arbitrary number of holes, answering affirmatively a conjecture from Blanchet-Sadri, Mercaş, and Scott.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Robert Mercaş
    • 2
  • Abraham Rashin
    • 3
  • Elara Willett
    • 4
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.GRLMCUniversitat Rovira i VirgiliTarragonaSpain
  3. 3.Department of MathematicsRutgers UniversityPiscatawayUSA
  4. 4.Department of MathematicsOberlin CollegeOberlinUSA

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