<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-02375068</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-12T14:21:05+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">On abelian saturated infinite words</title>
            <author role="aut">
              <persName>
                <forename type="first">Sergey</forename>
                <surname>Avgustinovich</surname>
              </persName>
              <email type="md5">bbb679ebdafb9452cbe16ded7c0701ab</email>
              <email type="domain">math.nsc.ru</email>
              <idno type="idhal" notation="numeric">972350</idno>
              <idno type="halauthorid" notation="string">1103082-972350</idno>
              <affiliation ref="#struct-82743"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Julien</forename>
                <surname>Cassaigne</surname>
              </persName>
              <email type="md5">755578b87d2c9388e7cda4872829712a</email>
              <email type="domain">math.cnrs.fr</email>
              <idno type="idhal" notation="numeric">954952</idno>
              <idno type="halauthorid" notation="string">128074-954952</idno>
              <affiliation ref="#struct-241321"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Juhani</forename>
                <surname>Karhumaki</surname>
              </persName>
              <idno type="halauthorid">214095-0</idno>
              <affiliation ref="#struct-300810"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Svetlana</forename>
                <surname>Puzynina</surname>
              </persName>
              <idno type="halauthorid">735692-0</idno>
              <affiliation ref="#struct-53198"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Aleksi</forename>
                <surname>Saarela</surname>
              </persName>
              <idno type="halauthorid">735689-0</idno>
              <affiliation ref="#struct-93061"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Julien</forename>
                <surname>Cassaigne</surname>
              </persName>
              <email type="md5">755578b87d2c9388e7cda4872829712a</email>
              <email type="domain">math.cnrs.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2020-12-29 19:12:54</date>
              <date type="whenModified">2025-11-06 08:50:02</date>
              <date type="whenReleased">2021-01-13 13:22:50</date>
              <date type="whenProduced">2019-11</date>
              <date type="whenEndEmbargoed">2020-12-29</date>
              <ref type="file" target="https://hal.science/hal-02375068v1/document">
                <date notBefore="2020-12-29"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-02375068v1/file/rich-20180110.pdf" id="file-3090592-2704374">
                <date notBefore="2020-12-29"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="34947">
                <persName>
                  <forename>Julien</forename>
                  <surname>Cassaigne</surname>
                </persName>
                <email type="md5">755578b87d2c9388e7cda4872829712a</email>
                <email type="domain">math.cnrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-02375068</idno>
            <idno type="halUri">https://hal.science/hal-02375068</idno>
            <idno type="halBibtex">avgustinovich:hal-02375068</idno>
            <idno type="halRefHtml">&lt;i&gt;Theoretical Computer Science&lt;/i&gt;, 2019, 792, pp.154-160. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.tcs.2018.05.013"&gt;&amp;#x27E8;10.1016/j.tcs.2018.05.013&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Theoretical Computer Science, 2019, 792, pp.154-160. &amp;#x27E8;10.1016/j.tcs.2018.05.013&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3090592-2704374"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="I2M">Institut de Mathématiques de Marseille</idno>
            <idno type="stamp" n="I2M-2014-" corresp="I2M">Institut de Mathématiques de Marseille 2014-</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">On abelian saturated infinite words</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Sergey</forename>
                    <surname>Avgustinovich</surname>
                  </persName>
                  <email type="md5">bbb679ebdafb9452cbe16ded7c0701ab</email>
                  <email type="domain">math.nsc.ru</email>
                  <idno type="idhal" notation="numeric">972350</idno>
                  <idno type="halauthorid" notation="string">1103082-972350</idno>
                  <affiliation ref="#struct-82743"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Julien</forename>
                    <surname>Cassaigne</surname>
                  </persName>
                  <email type="md5">755578b87d2c9388e7cda4872829712a</email>
                  <email type="domain">math.cnrs.fr</email>
                  <idno type="idhal" notation="numeric">954952</idno>
                  <idno type="halauthorid" notation="string">128074-954952</idno>
                  <affiliation ref="#struct-241321"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Juhani</forename>
                    <surname>Karhumaki</surname>
                  </persName>
                  <idno type="halauthorid">214095-0</idno>
                  <affiliation ref="#struct-300810"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Svetlana</forename>
                    <surname>Puzynina</surname>
                  </persName>
                  <idno type="halauthorid">735692-0</idno>
                  <affiliation ref="#struct-53198"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Aleksi</forename>
                    <surname>Saarela</surname>
                  </persName>
                  <idno type="halauthorid">735689-0</idno>
                  <affiliation ref="#struct-93061"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">19594</idno>
                <idno type="issn">0304-3975</idno>
                <idno type="eissn">1879-2294</idno>
                <title level="j">Theoretical Computer Science</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">792</biblScope>
                  <biblScope unit="pp">154-160</biblScope>
                  <date type="datePub">2019-11</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.tcs.2018.05.013</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info.info-dm">Computer Science [cs]/Discrete Mathematics [cs.DM]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Let f : Z + → R be an increasing function. We say that an infinite word w is abelian f (n)-saturated if each factor of length n contains Θ(f (n)) abelian nonequivalent factors. We show that binary infinite words cannot be abelian n 2saturated, but, for any ε &gt; 0, they can be abelian n 2−ε-saturated. There is also a sequence of finite words (w n), with |w n | = n, such that each w n contains at least Cn 2 abelian nonequivalent factors for some constant C &gt; 0. We also consider saturated words and their connection to palindromic richness in the case of equality and k-abelian equivalence.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-82743" status="VALID">
          <orgName>Sobolev Institute of Mathematics</orgName>
          <desc>
            <address>
              <addrLine>4 Acad. Koptyug avenue, 630090 Novosibirsk Russia</addrLine>
              <country key="RU"/>
            </address>
            <ref type="url">http://www.math.nsc.ru/english.html</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300194" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-241321" status="VALID">
          <idno type="RNSR">201420768T</idno>
          <idno type="ROR">042h2y225</idno>
          <orgName>Institut de Mathématiques de Marseille</orgName>
          <orgName type="acronym">I2M</orgName>
          <date type="start">2014</date>
          <desc>
            <address>
              <addrLine>Centre de Mathématiques et Informatique (CMI)Technopôle Château-Gombert39, rue Frédéric Joliot Curie13453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.i2m.univ-amu.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7373" active="#struct-198056" type="direct"/>
            <relation name="UMR7373" active="#struct-300415" type="direct"/>
            <relation name="UMR7373" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300810" status="VALID">
          <orgName>University of Turku</orgName>
          <desc>
            <address>
              <addrLine>20014 Turun yliopisto, Finland</addrLine>
              <country key="FI"/>
            </address>
            <ref type="url">http://www.utu.fi/en/Pages/home.aspx</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-53198" status="VALID">
          <orgName>Department of Mathematics</orgName>
          <desc>
            <address>
              <country key="FI"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-300810" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-93061" status="VALID">
          <orgName>Turku Centre for Computer Science</orgName>
          <desc>
            <address>
              <addrLine>FIN-20014, Turku</addrLine>
              <country key="FI"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-112126" type="direct"/>
            <relation active="#struct-300810" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300194" status="VALID">
          <idno type="ROR">https://ror.org/02frkq021</idno>
          <orgName>Siberian Branch of the Russian Academy of Sciences</orgName>
          <orgName type="acronym">SB RAS</orgName>
          <desc>
            <address>
              <addrLine>17, Ac. Lavrentieva ave., Novosibirsk, 630090</addrLine>
              <country key="RU"/>
            </address>
            <ref type="url">http://www.sbras.ru/en</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-112126" status="VALID">
          <idno type="ROR">https://ror.org/029pk6x14</idno>
          <orgName>Åbo Akademi University [Turku]</orgName>
          <desc>
            <address>
              <addrLine>Tuomiokirkontori 3FI-20500 Turku</addrLine>
              <country key="FI"/>
            </address>
            <ref type="url">http://www.abo.fi/public/en/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>