How Many Holes Can an Unbordered Partial Word Contain?

  • Francine Blanchet-Sadri
  • Emily Allen
  • Cameron Byrum
  • Robert Mercaş
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)


Partial words are sequences over a finite alphabet that may have some undefined positions, or “holes,” that are denoted by \(\ensuremath{\diamond}\)’s. A nonempty partial word is called bordered if one of its proper prefixes is compatible with one of its suffixes (here \(\ensuremath{\diamond}\) is compatible with every letter in the alphabet); it is called unbordered otherwise. In this paper, we investigate the problem of computing the maximum number of holes a partial word of a fixed length can have and still fail to be bordered.


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  1. 1.
    Berstel, J., Boasson, L.: Partial words and a theorem of Fine and Wilf. Theoretical Computer Science 218, 135–141 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press (2007)Google Scholar
  3. 3.
    Blanchet-Sadri, F.: Primitive partial words. Discrete Applied Mathematics 148, 195–213 (2005)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Blanchet-Sadri, F., Davis, C., Dodge, J., Mercaş, R., Moorefield, M.: Unbordered partial words. Discrete Applied Mathematics (2008), doi:10.1016/j.dam.2008.04.004Google Scholar
  5. 5.
    Blanchet-Sadri, F.: Open problems on partial words. In: Bel-Enguix, G., Jiménez-López, M., Martín-Vide, C. (eds.) New Developments in Formal Languages and Applications, pp. 11–58. Springer, Berlin (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Emily Allen
    • 2
  • Cameron Byrum
    • 3
  • Robert Mercaş
    • 4
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  3. 3.Department of MathematicsUniversity of MississippiUSA
  4. 4.GRLMCUniversitat Rovira i VirgiliTarragonaSpain

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