Bounds on Powers in Strings

Authors:
Maxime Crochemore;Szilárd Zsolt Fazekas;Costas Iliopoulos;Inuka Jayasekera
Affiliations:
King's College, London, U.K. and Université Paris-Est, France;Rovira i Virgili University, Tarragona, Spain;King's College, London, U.K.;King's College, London, U.K.
Venue:
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Year:
2008

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Abstract

We show a 茂戮驴(nlogn) bound on the maximal number of occurrences of primitively-rooted k-th powers occurring in a string of length nfor any integer k, k茂戮驴 2. We also show a 茂戮驴(n2) bound on the maximal number of primitively-rooted powers with fractional exponent e, 1 en. 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.