Bounds on Powers in Strings

  • Maxime Crochemore
  • Szilárd Zsolt Fazekas
  • Costas Iliopoulos
  • Inuka Jayasekera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)


We show a Θ(n logn) bound on the maximal number of occurrences of primitively-rooted k-th powers occurring in a string of length n for any integer k, k ≥ 2. We also show a Θ(n 2) bound on the maximal number of primitively-rooted powers with fractional exponent e, 1 < e < 2, occurring in a string of length n. This result holds obviously for their maximal number of occurrences. The first result contrasts with the linear number of occurrences of maximal repetitions of exponent at least 2.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Maxime Crochemore
    • 1
    • 2
  • Szilárd Zsolt Fazekas
    • 3
  • Costas Iliopoulos
    • 1
  • Inuka Jayasekera
    • 1
  1. 1.King’s CollegeLondonU.K.
  2. 2.Université Paris-EstFrance
  3. 3.Rovira i Virgili UniversityTarragonaSpain

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