Abelian Pattern Avoidance in Partial Words

  • Francine Blanchet-Sadri
  • Sean Simmons
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)

Abstract

Pattern avoidance is an important topic in combinatorics on words which dates back to the beginning of the twentieth century when Thue constructed an infinite word over a ternary alphabet that avoids squares, i.e., a word with no two adjacent identical factors. This result finds applications in various algebraic contexts where more general patterns than squares are considered. On the other hand, Erdős raised the question as to whether there exists an infinite word that avoids abelian squares, i.e., a word with no two adjacent factors being permutations of one another. Although this question was answered affirmately years later, knowledge of abelian pattern avoidance is rather limited. Recently, (abelian) pattern avoidance was initiated in the more general framework of partial words, which allow for undefined positions called holes. Here, we investigate conditions for a pattern to be abelian avoidable by a partial word with finitely or infinitely many holes.

Keywords

Distinct Variable Alphabet Size Pigeonhole Principle Partial Word Binary Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Sean Simmons
    • 2
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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