On maximal repetitions in words
Identifieur interne : 00A960 ( Main/Exploration ); précédent : 00A959; suivant : 00A961On maximal repetitions in words
Auteurs : Roman Kolpakov [Russie] ; Gregory Kucherov [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
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.
Url:
DOI: 10.1007/3-540-48321-7_31
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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.</div></front></TEI><affiliations><list><country><li>France</li><li>Russie</li></country><region><li>District fédéral central</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Moscou</li><li>Villers-lès-Nancy</li></settlement></list><tree><country name="Russie"><region name="District fédéral central"><name sortKey="Kolpakov, Roman" sort="Kolpakov, Roman" uniqKey="Kolpakov R" first="Roman" last="Kolpakov">Roman Kolpakov</name></region><name sortKey="Kolpakov, Roman" sort="Kolpakov, Roman" uniqKey="Kolpakov R" first="Roman" last="Kolpakov">Roman Kolpakov</name></country><country name="France"><region name="Grand Est"><name sortKey="Kucherov, Gregory" sort="Kucherov, Gregory" uniqKey="Kucherov G" first="Gregory" last="Kucherov">Gregory Kucherov</name></region><name sortKey="Kucherov, Gregory" sort="Kucherov, Gregory" uniqKey="Kucherov G" first="Gregory" last="Kucherov">Gregory Kucherov</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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