Long unavoidable patterns

  • Ursula Schmidt
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 210)


We examine long unavoidable patterns, unavoidable in the sense of Bean. Ehrenfeucht. McNulty. We prove that there is only one unavoidable pattern of length 2n−1 on an alphabet with n letters ; this pattern is a "quasi-power" in the sense of Schützenberger. We characterize the unavoidable words of length 2n−2 and 2n−3. Finally we show that every unavoidable word sufficiently long has a certain "quasi-power" as a subword.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bean D.R., Ehrenfeucht A., McNulty G.F., Avoidable patterns in strings of symbols. Pacific J. Math. 85 (1979), 261–294.Google Scholar
  2. [2]
    Berstel J., Some recent results on squarefree words, STACS 84, Springer Lecture Notes in Computer Science, Vol. 166 (1984), 14–25.Google Scholar
  3. [3]
    Main M.G., Lorentz R.J., An 0(n log n) Algorithm for Finding All Repetitions in a String, J. Algorithms 5 (1984), 422–432.CrossRefGoogle Scholar
  4. [4]
    Lothaire M., Combinatorics on Words, Addison-Wesley 1983.Google Scholar
  5. [5]
    Restivo A., Salemi S., On Weakly Square-free Words, Bull. EATCS 21 (1983), 49–56.Google Scholar
  6. [6]
    Schützenberger, M.P., On a Special Class of Recurrent Events, Annals Math. Stat. 32 (1961), 1201–1213.Google Scholar
  7. [7]
    Thue A., Uber unendliche Zeichenreihen, Norske Vid. Selsk. Skr., I. Mat. Nat. Kl., Christiania, 7 (1906), 1–22.Google Scholar
  8. [8]
    Thue A., Uber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr., I. Mat. Nat. KI., Christiania, 1 (1912), 1–67.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Ursula Schmidt
    • 1
  1. 1.LiTP, Université Paris VI Couloir 45-55PARIS Cedex 05

Personalised recommendations