<?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-01826868v2</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="2026-05-17T20:04:21+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Quasitrivial semigroups: Characterizations and enumerations</title>
            <author role="aut">
              <persName>
                <forename type="first">Miguel</forename>
                <surname>Couceiro</surname>
              </persName>
              <email type="md5">f529b06ac4780b9b07b39d207edbf60f</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">miguel-couceiro</idno>
              <idno type="idhal" notation="numeric">1498</idno>
              <idno type="halauthorid" notation="string">17246-1498</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2316-7623</idno>
              <idno type="IDREF">https://www.idref.fr/223362395</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=6w-xX8sAAAAJ</idno>
              <affiliation ref="#struct-205125"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jimmy</forename>
                <surname>Devillet</surname>
              </persName>
              <idno type="halauthorid">1118856-0</idno>
              <affiliation ref="#struct-264920"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean-Luc</forename>
                <surname>Marichal</surname>
              </persName>
              <email type="md5">84e9504042ff646eb0969ced1bf8f8b4</email>
              <email type="domain">uni.lu</email>
              <idno type="idhal" notation="numeric">908349</idno>
              <idno type="halauthorid" notation="string">129710-908349</idno>
              <idno type="IDREF">https://www.idref.fr/139934766</idno>
              <affiliation ref="#struct-264920"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Miguel</forename>
                <surname>Couceiro</surname>
              </persName>
              <email type="md5">1090c3ea2d8280fa0028311c6ba45d22</email>
              <email type="domain">loria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2018-06-30 00:02:58</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2018-07-02 15:53:23</date>
              <date type="whenWritten">2017</date>
              <date type="whenModified">2025-11-04 12:04:57</date>
              <date type="whenReleased">2018-07-02 15:57:59</date>
              <date type="whenProduced">2019-06-01</date>
              <date type="whenEndEmbargoed">2018-07-02</date>
              <ref type="file" target="https://inria.hal.science/hal-01826868v2/document">
                <date notBefore="2018-07-02"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/hal-01826868v2/file/QuasitrivialSemigroups%20-%20Revised2.pdf" id="file-1827715-1855506">
                <date notBefore="2018-07-02"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="304220">
                <persName>
                  <forename>Miguel</forename>
                  <surname>Couceiro</surname>
                </persName>
                <email type="md5">1090c3ea2d8280fa0028311c6ba45d22</email>
                <email type="domain">loria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01826868</idno>
            <idno type="halUri">https://inria.hal.science/hal-01826868</idno>
            <idno type="halBibtex">couceiro:hal-01826868</idno>
            <idno type="halRefHtml">&lt;i&gt;Semigroup Forum&lt;/i&gt;, 2019, 98 (3), pp.472-498. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s00233-018-9928-3"&gt;&amp;#x27E8;10.1007/s00233-018-9928-3&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Semigroup Forum, 2019, 98 (3), pp.472-498. &amp;#x27E8;10.1007/s00233-018-9928-3&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1827715-1855506"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="LORIA2">Publications du LORIA</idno>
            <idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="CENTRALESUPELEC">Ecole CentraleSupélec</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="LORIA">Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
            <idno type="stamp" n="LORIA-NLPKD" corresp="LORIA">Department of Natural Language Processing &amp; Knowledge Discovery</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="CENTRALESUPELEC-SACLAY" corresp="UNIV-PARIS-SACLAY">CENTRALESUPELEC-SACLAY</idno>
            <idno type="stamp" n="INRIAARTDOI">INRIAARTDOI</idno>
            <idno type="stamp" n="AM2I-UL">Pôle scientifique Automatique, Mathématiques, Informatique et leurs Intéractions de l'Université de Lorraine</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">Quasitrivial semigroups: Characterizations and enumerations</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Miguel</forename>
                    <surname>Couceiro</surname>
                  </persName>
                  <email type="md5">f529b06ac4780b9b07b39d207edbf60f</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">miguel-couceiro</idno>
                  <idno type="idhal" notation="numeric">1498</idno>
                  <idno type="halauthorid" notation="string">17246-1498</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2316-7623</idno>
                  <idno type="IDREF">https://www.idref.fr/223362395</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=6w-xX8sAAAAJ</idno>
                  <affiliation ref="#struct-205125"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jimmy</forename>
                    <surname>Devillet</surname>
                  </persName>
                  <idno type="halauthorid">1118856-0</idno>
                  <affiliation ref="#struct-264920"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-Luc</forename>
                    <surname>Marichal</surname>
                  </persName>
                  <email type="md5">84e9504042ff646eb0969ced1bf8f8b4</email>
                  <email type="domain">uni.lu</email>
                  <idno type="idhal" notation="numeric">908349</idno>
                  <idno type="halauthorid" notation="string">129710-908349</idno>
                  <idno type="IDREF">https://www.idref.fr/139934766</idno>
                  <affiliation ref="#struct-264920"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">10288</idno>
                <idno type="issn">0037-1912</idno>
                <idno type="eissn">1432-2137</idno>
                <title level="j">Semigroup Forum</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">98</biblScope>
                  <biblScope unit="issue">3</biblScope>
                  <biblScope unit="pp">472-498</biblScope>
                  <date type="datePub">2019-06-01</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/s00233-018-9928-3</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Quasitrivial semigroup</term>
                <term xml:lang="en">Single-plateaued weak ordering</term>
                <term xml:lang="en">Single-peaked ordering</term>
                <term xml:lang="en">Enumeration of quasitrivial semigroups</term>
                <term xml:lang="en">Quasitrivial and order-preserving semigroup</term>
                <term xml:lang="en">Quasitrivial and commutative semigroup</term>
              </keywords>
              <classCode scheme="halDomain" n="math">Mathematics [math]</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 investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-205125" status="OLD">
          <idno type="RNSR">200818291B</idno>
          <orgName>Knowledge  representation, reasonning</orgName>
          <orgName type="acronym">ORPAILLEUR</orgName>
          <date type="start">2008-01-01</date>
          <date type="end">2020-06-30</date>
          <desc>
            <address>
              <addrLine>Centre Inria de l'Université de Lorraine , 615 Rue du Jardin-Botanique, 54600 Villers-lès-Nancy</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/orpailleur</ref>
          </desc>
          <listRelation>
            <relation active="#struct-129671" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-423086" type="direct"/>
            <relation active="#struct-206040" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation active="#struct-413289" type="indirect"/>
            <relation name="UMR7503" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="department" xml:id="struct-264920" status="VALID">
          <orgName>Faculty of Science, Technology and Communication [Luxembourg]</orgName>
          <orgName type="acronym">FSTC</orgName>
          <desc>
            <address>
              <addrLine>Campus Kirchberg6, rue Richard Coudenhove-KalergiL-1359 Luxembourg</addrLine>
              <country key="LU"/>
            </address>
            <ref type="url">http://wwwen.uni.lu/fstc</ref>
          </desc>
          <listRelation>
            <relation active="#struct-366875" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-129671" status="VALID">
          <idno type="RNSR">198618246Y</idno>
          <idno type="ROR">https://ror.org/03fcjvn64</idno>
          <orgName>Centre Inria de l'Université de Lorraine</orgName>
          <desc>
            <address>
              <addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/nancy</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" 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="department" xml:id="struct-423086" status="VALID">
          <orgName>Department of Natural Language Processing &amp; Knowledge Discovery</orgName>
          <orgName type="acronym">LORIA - NLPKD</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.loria.fr/en/research/departments/natural-language-processing-and-knowledge-discovery/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-206040" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation active="#struct-413289" type="indirect"/>
            <relation name="UMR7503" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-206040" status="VALID">
          <idno type="IdRef">067077927</idno>
          <idno type="ISNI">0000000121795429</idno>
          <idno type="RNSR">198912571S</idno>
          <idno type="IdUnivLorraine">[UL]RSI--</idno>
          <idno type="ROR">https://ror.org/02vnf0c38</idno>
          <orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
          <orgName type="acronym">LORIA</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.loria.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-411575" type="direct"/>
            <relation active="#struct-413289" type="direct"/>
            <relation name="UMR7503" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-411575" status="VALID">
          <idno type="IdRef">184443237</idno>
          <idno type="ROR">https://ror.org/019tcpt25</idno>
          <orgName>CentraleSupélec</orgName>
          <desc>
            <address>
              <addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.centralesupelec.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-413289" status="VALID">
          <idno type="IdRef">157040569</idno>
          <idno type="IdUnivLorraine">[UL]100--</idno>
          <idno type="ROR">https://ror.org/04vfs2w97</idno>
          <orgName>Université de Lorraine</orgName>
          <orgName type="acronym">UL</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lorraine.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-366875" status="VALID">
          <idno type="IdRef">124635016</idno>
          <idno type="ISNI">0000000122959843</idno>
          <idno type="ROR">https://ror.org/036x5ad56</idno>
          <idno type="Wikidata">Q59668</idno>
          <orgName>Université du Luxembourg = University of Luxembourg = Universität Luxemburg</orgName>
          <orgName type="acronym">uni.lu</orgName>
          <date type="start">2003-01-01</date>
          <desc>
            <address>
              <addrLine>Université du Luxembourg [Siège] – 2, place de l’Université – L-4365 Esch-sur-Alzette – Luxembourg</addrLine>
              <country key="LU"/>
            </address>
            <ref type="url">http://wwwfr.uni.lu/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>