Overlap-freeness in infinite partial words

  • Authors:

  • Vesa Halava;Tero Harju;Tomi Kärki;Patrice Séébold

  • Affiliations:

  • Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland;Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland;Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland;LIRMM, UMR 5506 CNRS, 161 rue Ada 34392 Montpellier, France and Département Mathématiques et Informatique Appliquées, Université Paul Valéry, Route de Mende, 34199 Montpel ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

Quantified Score

Hi-index 5.23

Visualization

Abstract

We prove that there exist infinitely many infinite overlap-free binary partial words containing at least one hole. Moreover, we show that these words cannot contain more than one hole and the only hole must occur either in the first or in the second position. We define that a partial word is k-overlap-free if it does not contain a factor of the form xyxyx where the length of x is at least k. We prove that there exist infinitely many 2-overlap-free binary partial words containing an infinite number of holes.