Minimum Number of Holes in Unavoidable Sets of Partial Words of Size Three

  • Francine Blanchet-Sadri
  • Bob Chen
  • Aleksandar Chakarov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. In this paper, we consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem of fully characterizing all unavoidable sets of partial words of size three.


Conjugacy Class Equal Length Cayley Graph Mathematical Linguistics Discrete Apply Mathematic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Bob Chen
    • 2
  • Aleksandar Chakarov
    • 3
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of MathematicsUniversity of CaliforniaLaJollaUSA
  3. 3.Department of Computer ScienceUniversity of ColoradoBoulderUSA

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