On maximal repetitions in words
Identifieur interne : 002398 ( Istex/Corpus ); précédent : 002397; suivant : 002399On maximal repetitions in words
Auteurs : Roman Kolpakov ; Gregory KucherovSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
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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ISTEX:9A43E6F9F97663C764224D0C2E33B8AA421A35D7Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">On maximal repetitions in words</title><author><name sortKey="Kolpakov, Roman" sort="Kolpakov, Roman" uniqKey="Kolpakov R" first="Roman" last="Kolpakov">Roman Kolpakov</name><affiliation><mods:affiliation>French-Russian Institute for Informatics and Applied Mathematics, Moscow University, 119899, Moscow, Russia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: roman@vertex.inria.msu.ru</mods:affiliation></affiliation></author><author><name sortKey="Kucherov, Gregory" sort="Kucherov, Gregory" uniqKey="Kucherov G" first="Gregory" last="Kucherov">Gregory Kucherov</name><affiliation><mods:affiliation>LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101, 54602, Villers-lès-Nancy, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: kucherov@loria.fr</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:9A43E6F9F97663C764224D0C2E33B8AA421A35D7</idno><date when="1999" year="1999">1999</date><idno type="doi">10.1007/3-540-48321-7_31</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-6TKPBL9M-3/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">002398</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002398</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On maximal repetitions in words</title><author><name sortKey="Kolpakov, Roman" sort="Kolpakov, Roman" uniqKey="Kolpakov R" first="Roman" last="Kolpakov">Roman Kolpakov</name><affiliation><mods:affiliation>French-Russian Institute for Informatics and Applied Mathematics, Moscow University, 119899, Moscow, Russia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: roman@vertex.inria.msu.ru</mods:affiliation></affiliation></author><author><name sortKey="Kucherov, Gregory" sort="Kucherov, Gregory" uniqKey="Kucherov G" first="Gregory" last="Kucherov">Gregory Kucherov</name><affiliation><mods:affiliation>LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101, 54602, Villers-lès-Nancy, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: kucherov@loria.fr</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>Roman Kolpakov</name><affiliations><json:string>French-Russian Institute for Informatics and Applied Mathematics, Moscow University, 119899, Moscow, Russia</json:string><json:string>E-mail: roman@vertex.inria.msu.ru</json:string></affiliations></json:item><json:item><name>Gregory Kucherov</name><affiliations><json:string>LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101, 54602, Villers-lès-Nancy, France</json:string><json:string>E-mail: kucherov@loria.fr</json:string></affiliations></json:item></author><arkIstex>ark:/67375/HCB-6TKPBL9M-3</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: A (fractional) repetition in a word w is a subword with the period of at most half of the subword length. 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We study maximal repetitions occurring in <hi rend="italic">w</hi>, that is those for which any extended subword of <hi rend="italic">w</hi> has a bigger period. The set of such repetitions represents in a compact way all repetitions in <hi rend="italic">w</hi>.</p><p>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. 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We study maximal repetitions occurring in <Emphasis Type="Italic">w</Emphasis>, that is those for which any extended subword of <Emphasis Type="Italic">w</Emphasis> has a bigger period. The set of such repetitions represents in a compact way all repetitions in <Emphasis Type="Italic">w</Emphasis>.</Para><Para>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 <Emphasis Type="Italic">n</Emphasis> is linearly-bounded in n, and we mention some applications and consequences of this result.</Para></Abstract><ArticleNote Type="Misc"><Heading>Article</Heading><SimplePara>The work has been done during the first author’s visit of LORIA/INRIA-Lorraine supported by a grant from the French Ministry of Public Education and Research. The first author has been also in part supported by the Russian Foundation of Fundamental Research, under grant 96-01-01068, and by the Russian Federal Programme “Integration”, under grant 473. The work has been done within a joint project of the French-Russian A.M.Liapunov Institut of Applied Mathematics and Informatics at Moscow University</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On maximal repetitions in words</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>On maximal repetitions in words</title></titleInfo><name type="personal"><namePart type="given">Roman</namePart><namePart type="family">Kolpakov</namePart><affiliation>French-Russian Institute for Informatics and Applied Mathematics, Moscow University, 119899, Moscow, Russia</affiliation><affiliation>E-mail: roman@vertex.inria.msu.ru</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Gregory</namePart><namePart type="family">Kucherov</namePart><affiliation>LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101, 54602, Villers-lès-Nancy, France</affiliation><affiliation>E-mail: kucherov@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">1999</dateIssued><copyrightDate encoding="w3cdtf">1999</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">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.</abstract><relatedItem type="host"><titleInfo><title>Fundamentals of Computation Theory</title><subTitle>12th International Symposium, FCT’99 Iaşi, Romania, August 30 - September 3, 1999 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Gabriel</namePart><namePart type="family">Ciobanu</namePart><affiliation>Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania</affiliation><affiliation>E-mail: gabriel@info.uaic.ro</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Gheorghe</namePart><namePart type="family">Păun</namePart><affiliation>Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania</affiliation><affiliation>E-mail: gpaun@imar.ro</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1999</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16005">Theory of Computation</topic><topic authority="SpringerSubjectCodes" authorityURI="I17028">Discrete Mathematics in Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I15017">Data Structures</topic></subject><identifier type="DOI">10.1007/3-540-48321-7</identifier><identifier type="ISBN">978-3-540-66412-3</identifier><identifier type="eISBN">978-3-540-48321-2</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="BookTitleID">59698</identifier><identifier type="BookID">3-540-48321-7</identifier><identifier type="BookChapterCount">47</identifier><identifier type="BookVolumeNumber">1684</identifier><identifier type="BookSequenceNumber">1684</identifier><part><date>1999</date><detail type="volume"><number>1684</number><caption>vol.</caption></detail><extent unit="pages"><start>374</start><end>385</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 1999</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><affiliation>Karlsruhe University, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><affiliation>Cornell University, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jan</namePart><namePart type="family">van Leeuwen</namePart><affiliation>Utrecht University, The Netherlands</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1999</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 1999</recordOrigin></recordInfo></relatedItem><identifier type="istex">9A43E6F9F97663C764224D0C2E33B8AA421A35D7</identifier><identifier type="ark">ark:/67375/HCB-6TKPBL9M-3</identifier><identifier type="DOI">10.1007/3-540-48321-7_31</identifier><identifier type="ChapterID">31</identifier><identifier type="ChapterID">Chap31</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 1999</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-RLRX46XW-4">springer</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 1999</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/HCB-6TKPBL9M-3/record.json</uri></json:item></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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