On maximal repetitions in words
Identifieur interne : 00B163 ( Main/Merge ); précédent : 00B162; suivant : 00B164On maximal repetitions in words
Auteurs : R. Kolpakov [Russie] ; G. Kucherov [France]Source :
- Lecture notes in computer science [ 0302-9743 ] ; 1999.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
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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Pascal:99-0526090Le document en format XML
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Kucherov</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101</s1><s2>54602 Villers-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">99-0526090</idno><date when="1999">1999</date><idno type="stanalyst">PASCAL 99-0526090 INIST</idno><idno type="RBID">Pascal:99-0526090</idno><idno type="wicri:Area/PascalFrancis/Corpus">000A89</idno><idno type="wicri:Area/PascalFrancis/Curation">000D81</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000A75</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000A75</idno><idno type="wicri:doubleKey">0302-9743:1999:Kolpakov R:on:maximal:repetitions</idno><idno type="wicri:Area/Main/Merge">00B163</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">On maximal repetitions in words </title><author><name sortKey="Kolpakov, R" sort="Kolpakov, R" uniqKey="Kolpakov R" first="R." last="Kolpakov">R. Kolpakov</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>French-Russian Institute for Informatics and Applied Mathematics, Moscow University</s1><s2>119899 Moscow</s2><s3>RUS</s3><sZ>1 aut.</sZ></inist:fA14><country>Russie</country><placeName><settlement type="city">Moscou</settlement><region>District fédéral central</region></placeName></affiliation></author><author><name sortKey="Kucherov, G" sort="Kucherov, G" uniqKey="Kucherov G" first="G." last="Kucherov">G. Kucherov</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101</s1><s2>54602 Villers-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno><imprint><date when="1999">1999</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithmics</term><term>Linear time</term><term>Repetition</term><term>Word length</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Répétition</term><term>Longueur mot</term><term>Temps linéaire</term><term>Algorithmique</term><term>Maximal repetition in word</term><term>Mot Fibonacci</term><term>Mot binaire</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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.</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, R" sort="Kolpakov, R" uniqKey="Kolpakov R" first="R." last="Kolpakov">R. Kolpakov</name></region></country><country name="France"><region name="Grand Est"><name sortKey="Kucherov, G" sort="Kucherov, G" uniqKey="Kucherov G" first="G." last="Kucherov">G. Kucherov</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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