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On Maximal Repetitions in Words

Roman Kolpakov Gregory Kucherov 1
1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : A (fractional) repetition in a word $w$ is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in $w$, that is those for which any extended subword of $w$ has a bigger period. The set of such repetitions represents in a compact way all repetitions in $w$. We first study maximal repetitions in Fibonacci words -- we count their exact number, and estimate the sum of their exponents. These quantities turn out to be linearly-bounded in the length of the word. We then prove that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length $n$ is linearly-bounded in $n$, and we mention some applications and consequences of this result.
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https://hal.inria.fr/inria-00098852
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Submitted on : Tuesday, September 26, 2006 - 8:39:16 AM
Last modification on : Friday, February 26, 2021 - 3:28:02 PM

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  • HAL Id : inria-00098852, version 1

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Roman Kolpakov, Gregory Kucherov. On Maximal Repetitions in Words. 12th International Symposium on Fundamentals of Computation Theory - FCT'99, 1999, Iasi Romania, pp.374 -- 385. ⟨inria-00098852⟩

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