Skip to main content
SpringerLink
Log in

Long unavoidable patterns

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

We examine long unavoidable patterns, unavoidable in the sense of Bean, Ehrenfeucht, McNulty. Zimin and independently Schmidt have shown 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 sufficiently long unavoidable word has a certain “quasi-power” as a subword.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bean, D.R., Ehrenfeucht, A., McNulty, G.F.: Avoidable Patterns in Strings of Symbols. Pacific J. Math. 85, 261–294 (1979)

    Google Scholar 

  2. Berstel, J.: Some recent results on square-free words. STACS 84. Lect. Notes Comput. Sci. Vol. 166, pp. 14–25, Berlin, Heidelberg, New York: Springer 1984

    Google Scholar 

  3. Main, M.G., Lorentz, R.J.: An O( n log n ) Algorithm for Finding All Repetitions in a String. J. Algorithms 5, 422–432 (1984)

    Google Scholar 

  4. Lothaire: Combinatorics on Words. Addison-Wesley 1983

  5. Restivo, A., Salemi, S.: On Weakly Square-free Words. Bull. EATCS 21, 49–56 (1983)

    Google Scholar 

  6. Schmidt, U.: Motifs inévitables longs. Rapport LITP 85-47, Université Paris 6, Paris 1985

    Google Scholar 

  7. Schützenberger, M.P.: On a Special Class of Recurrent Events. Annals Math. Stat. 32, 1201–1213 (1961)

    Google Scholar 

  8. Thue, A.: Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr., I. Math. Nat. Kl., Christiania 7, 1–22 (1906)

    Google Scholar 

  9. Thue, A.: Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr., I. Mat. Nat. Kl., Christiania 1, 1–67 (1912)

    Google Scholar 

  10. Zimin, A.I.: Blocking sets of terms. Matem. Sbornik tom. 119 (161) (1982); Engl. trans. Math. USSR Sbornik 47, 353–364 (1984)

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Universität Karlsruhe, Postfach 6980, D-7500, Karlsruhe 1, Federal Republic of Germany

    Ursula Schmidt

Authors
  1. Ursula Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was done while the author stayed at LITP, Université Paris 6, France

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schmidt, U. Long unavoidable patterns. Acta Informatica 24, 433–445 (1987). https://doi.org/10.1007/BF00292112

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00292112

Keywords

Search

Navigation