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Restricted Square Property and Infinite Partial Words

Vesa Halava, Tero Harju, Tomi Kärki, Patrice Séébold, Restricted Square Property and Infinite Partial Words. TUCS Technical Reports 930, Turku Centre for Computer Science, 2009.

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.

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BibTeX entry:

@TECHREPORT{tHaHaKaSe09a,
  title = {Restricted Square Property and Infinite Partial Words},
  author = {Halava, Vesa and Harju, Tero and Kärki, Tomi and Séébold, Patrice},
  number = {930},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2009},
  keywords = {repetition-freeness, k-free, overlap, partial words, Thue-Morse word, infinite words, restricted square property},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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