<?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-03658172</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="2026-05-17T10:46:01+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Weakly and Strongly Aperiodic Subshifts of Finite Type on Baumslag-Solitar Groups</title>
            <author role="aut">
              <persName>
                <forename type="first">Solène</forename>
                <surname>Esnay</surname>
              </persName>
              <idno type="halauthorid">2493447-0</idno>
              <affiliation ref="#struct-544673"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Etienne</forename>
                <surname>Moutot</surname>
              </persName>
              <email type="md5">519f14eb29c418a75b3a17efd2c9f23e</email>
              <email type="domain">ens-lyon.org</email>
              <idno type="idhal" notation="string">etienne-moutot</idno>
              <idno type="idhal" notation="numeric">169567</idno>
              <idno type="halauthorid" notation="string">39947-169567</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2073-4709</idno>
              <affiliation ref="#struct-441569"/>
              <affiliation ref="#struct-241321"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Etienne</forename>
                <surname>Moutot</surname>
              </persName>
              <email type="md5">897cb62303eb5bc2c24c178064e09391</email>
              <email type="domain">math.cnrs.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2022-05-03 16:09:17</date>
              <date type="whenModified">2025-10-13 09:44:15</date>
              <date type="whenReleased">2022-05-04 15:26:06</date>
              <date type="whenProduced">2022-05-25</date>
              <date type="whenEndEmbargoed">2022-05-03</date>
              <ref type="file" target="https://hal.science/hal-03658172v1/document">
                <date notBefore="2022-05-03"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03658172v1/file/esnaymoutot22.pdf" id="file-3658172-3194310">
                <date notBefore="2022-05-03"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2105.00784"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="467749">
                <persName>
                  <forename>Etienne</forename>
                  <surname>Moutot</surname>
                </persName>
                <email type="md5">897cb62303eb5bc2c24c178064e09391</email>
                <email type="domain">math.cnrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03658172</idno>
            <idno type="halUri">https://hal.science/hal-03658172</idno>
            <idno type="halBibtex">esnay:hal-03658172</idno>
            <idno type="halRefHtml">&lt;i&gt;Theoretical Computer Science&lt;/i&gt;, 2022, 917, pp.31-50. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.tcs.2022.03.010"&gt;&amp;#x27E8;10.1016/j.tcs.2022.03.010&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Theoretical Computer Science, 2022, 917, pp.31-50. &amp;#x27E8;10.1016/j.tcs.2022.03.010&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3658172-3194310"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENS-LYON">École Normale Supérieure de Lyon</idno>
            <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="UNIV-LYON1">Université Claude Bernard - Lyon I</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="LIP" corresp="UNIV-LYON1">Laboratoire de l'Informatique du Parallélisme</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>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</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">Weakly and Strongly Aperiodic Subshifts of Finite Type on Baumslag-Solitar Groups</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Solène</forename>
                    <surname>Esnay</surname>
                  </persName>
                  <idno type="halauthorid">2493447-0</idno>
                  <affiliation ref="#struct-544673"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Etienne</forename>
                    <surname>Moutot</surname>
                  </persName>
                  <email type="md5">519f14eb29c418a75b3a17efd2c9f23e</email>
                  <email type="domain">ens-lyon.org</email>
                  <idno type="idhal" notation="string">etienne-moutot</idno>
                  <idno type="idhal" notation="numeric">169567</idno>
                  <idno type="halauthorid" notation="string">39947-169567</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2073-4709</idno>
                  <affiliation ref="#struct-441569"/>
                  <affiliation ref="#struct-241321"/>
                </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">917</biblScope>
                  <biblScope unit="pp">31-50</biblScope>
                  <date type="datePub">2022-05-25</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2105.00784</idno>
              <idno type="doi">10.1016/j.tcs.2022.03.010</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Groups</term>
                <term xml:lang="en">Substitutions</term>
                <term xml:lang="en">Cayley graphs</term>
                <term xml:lang="en">Tilings</term>
                <term xml:lang="en">Subshift of finite type</term>
                <term xml:lang="en">Aperiodicity</term>
                <term xml:lang="en">Symbolic dynamics</term>
              </keywords>
              <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>We study the periodicity of subshifts of finite type (SFT) on Baumslag-Solitar groups. We show that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs. In particular, this shows that unlike Z 2 , but like Z 3 , strong and weak aperiodic SFTs are different classes of SFTs in residually finite BS groups. More precisely, we prove that a weakly aperiodic SFT on BS(m,n) due to Aubrun and Kari is, in fact, strongly aperiodic on BS(1,n); and weakly but not strongly aperiodic on any other BS(m,n). In addition, we exhibit an SFT which is weakly but not strongly aperiodic on BS(1,n); and we show that there exists a strongly aperiodic SFT on BS(n,n).</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-544673" status="VALID">
          <orgName>Modèles de calcul, Complexité, Combinatoire</orgName>
          <orgName type="acronym">MC2</orgName>
          <desc>
            <address>
              <addrLine>ENS Lyon 46 allée d'Italie 69364 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-lyon.fr/LIP/MC2/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-35418" type="direct"/>
            <relation active="#struct-6818" type="indirect"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation active="#struct-194495" type="indirect"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation name="UMR5668 / URA1398" active="#struct-441569" type="indirect"/>
          </listRelation>
        </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="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="laboratory" xml:id="struct-35418" status="VALID">
          <idno type="IdRef">191041289</idno>
          <idno type="ISNI">0000000104538607</idno>
          <idno type="RNSR">200317503S</idno>
          <idno type="ROR">04msnz457</idno>
          <orgName>Laboratoire de l'Informatique du Parallélisme</orgName>
          <orgName type="acronym">LIP</orgName>
          <date type="start">1990-01-01</date>
          <desc>
            <address>
              <addrLine>46 Allée d'Italie 69364 LYON CEDEX 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-lyon.fr/LIP/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-6818" type="direct"/>
            <relation active="#struct-301088" type="direct"/>
            <relation active="#struct-194495" type="direct"/>
            <relation active="#struct-300009" type="direct"/>
            <relation name="UMR5668 / URA1398" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-6818" status="VALID">
          <idno type="IdRef">149154992</idno>
          <idno type="ISNI">0000000123319856</idno>
          <idno type="ROR">https://ror.org/04zmssz18</idno>
          <idno type="Wikidata">Q10159</idno>
          <orgName>École normale supérieure de Lyon</orgName>
          <orgName type="acronym">ENS de Lyon</orgName>
          <date type="start">2010-01-01</date>
          <desc>
            <address>
              <addrLine>15 parvis René Descartes - BP 7000 - 69342 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301088" status="VALID">
          <idno type="ROR">https://ror.org/01rk35k63</idno>
          <orgName>Université de Lyon</orgName>
          <desc>
            <address>
              <addrLine>92 rue Pasteur - CS 30122, 69361 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-lyon.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-194495" status="VALID">
          <idno type="IdRef">026402823</idno>
          <idno type="ISNI">0000000121686185</idno>
          <idno type="ROR">https://ror.org/029brtt94</idno>
          <orgName>Université Claude Bernard Lyon 1</orgName>
          <orgName type="acronym">UCBL</orgName>
          <desc>
            <address>
              <addrLine>43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lyon1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/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>
      </listOrg>
    </back>
  </text>
</TEI>