Abelian Square-Free Partial Words

  • Francine Blanchet-Sadri
  • Jane I. Kim
  • Robert Mercaş
  • William Severa
  • Sean Simmons
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)


Erdös raised the question whether there exist infinite abelian square-free words over a given alphabet (words in which no two adjacent subwords are permutations of each other). Infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words (sequences that may contain some holes). In particular, we give lower and upper bounds for the number of letters needed to construct infinite abelian square-free partial words with finitely or infinitely many holes. In the case of one hole, we prove that the minimal alphabet size is four, while in the case of more than one hole, we prove that it is five.


Alphabet Size Partial Word Binary Alphabet Doklady Akademii Nauk SSSR Full Word 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Jane I. Kim
    • 2
  • Robert Mercaş
    • 3
  • William Severa
    • 4
  • Sean Simmons
    • 5
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of MathematicsColumbia UniversityNew YorkUSA
  3. 3.Harriet L. Wilkes Honors CollegeFlorida Atlantic UniversityJupiterUSA
  4. 4.Departament de Filologies RomàniquesGRLMC, Universitat Rovira i VirgiliTarragonaSpain
  5. 5.Department of MathematicsUniversity of Texas at AustinAustinUSA

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