Abstract
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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Crochemore, M., Fazekas, S.Z., Iliopoulos, C., Jayasekera, I. (2008). Bounds on Powers in Strings. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_16
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DOI: https://doi.org/10.1007/978-3-540-85780-8_16
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