NUMBER OF OCCURRENCES OF POWERS IN STRINGS-Reference-Cited by-同舟云学术

NUMBER OF OCCURRENCES OF POWERS IN STRINGS

Published:2010-08 Issue:04 Volume:21 Page:535-547
ISSN:0129-0541
Container-title:International Journal of Foundations of Computer Science
language:en
Short-container-title:Int. J. Found. Comput. Sci.

Author:

CROCHEMORE MAXIME¹²,FAZEKAS SZILÁRD ZSOLT³,ILIOPOULOS COSTAS S.⁴,JAYASEKERA INUKA⁴

Affiliation:

1. Institut Gaspard-Monge, Université de Marne-la-Vallée, F-77454 Marne-la-Vallée, Cedex 2, France

2. Department of Computer Science, King's College London, Strand, London WC2R 2LS, UK

3. Institute of Mathematics and Computer Science, University College of Nyíregyháza, Sóstói út 31./B, 4400 Nyíregyháza, Hungary

4. Algorithm Design Group, Department of Computer Science, King's College London, Strand, London WC2R 2LS, England

Abstract

We show a Θ(n log n) 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(n2) 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129054110007416

Reference10 articles.

1. Optimal off-line detection of repetitions in a string

2. An optimal algorithm for computing the repetitions in a word

3. Squares, cubes, and time-space efficient string searching

4. A characterization of the squares in a Fibonacci string

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