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Conference Papers Year : 1999

On Maximal Repetitions in Words

Roman Kolpakov
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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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inria-00098852 , version 1 (26-09-2006)


  • HAL Id : inria-00098852 , version 1


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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