<?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-05349115</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="2026-05-24T06:07:49+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">On the generating series of the degree sequence</title>
            <author role="aut">
              <persName>
                <forename type="first">Quang-Khai</forename>
                <surname>Nguyen</surname>
              </persName>
              <email type="md5">57d3ac5ced45cf87a5d00113c234d50e</email>
              <email type="domain">math.univ-lyon.fr</email>
              <idno type="idhal" notation="numeric">1604103</idno>
              <idno type="halauthorid" notation="string">3870612-1604103</idno>
              <affiliation ref="#struct-193738"/>
              <affiliation ref="#struct-521751"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Quang-Khai</forename>
                <surname>Nguyen</surname>
              </persName>
              <email type="md5">1844f4e62cd7561ba760e222c0173fbe</email>
              <email type="domain">univ-lyon1.fr</email>
            </editor>
            <funder>Co-Funded by the European Union MSCA-Horizon Europe, grant agreement No. 101126554</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-11-05 13:18:30</date>
              <date type="whenModified">2026-04-29 16:18:22</date>
              <date type="whenReleased">2025-11-06 10:05:31</date>
              <date type="whenProduced">2025-11-05</date>
              <date type="whenEndEmbargoed">2025-11-05</date>
              <ref type="file" target="https://hal.science/hal-05349115v1/document">
                <date notBefore="2025-11-05"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-05349115v1/file/On_the_generating_series_of_the_degree_sequences_Hal.pdf" id="file-5349115-4577991">
                <date notBefore="2025-11-05"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2510.06142"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1710584">
                <persName>
                  <forename>Quang-Khai</forename>
                  <surname>Nguyen</surname>
                </persName>
                <email type="md5">1844f4e62cd7561ba760e222c0173fbe</email>
                <email type="domain">univ-lyon1.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-05349115</idno>
            <idno type="halUri">https://hal.science/hal-05349115</idno>
            <idno type="halBibtex">nguyen:hal-05349115</idno>
            <idno type="halRefHtml">2025</idno>
            <idno type="halRef">2025</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-5349115-4577991"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-ST-ETIENNE">Université Jean Monnet - Saint-Etienne</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="ICJ" corresp="UNIV-LYON1">Institut Camille Jordan</idno>
            <idno type="stamp" n="UNIV-LYON1">Université Claude Bernard - Lyon I</idno>
            <idno type="stamp" n="INSA-LYON">Institut National des Sciences Appliquées de Lyon</idno>
            <idno type="stamp" n="EC-LYON">Ecole Centrale de Lyon</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">On the generating series of the degree sequence</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Quang-Khai</forename>
                    <surname>Nguyen</surname>
                  </persName>
                  <email type="md5">57d3ac5ced45cf87a5d00113c234d50e</email>
                  <email type="domain">math.univ-lyon.fr</email>
                  <idno type="idhal" notation="numeric">1604103</idno>
                  <idno type="halauthorid" notation="string">3870612-1604103</idno>
                  <affiliation ref="#struct-193738"/>
                  <affiliation ref="#struct-521751"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">2510.06142</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Dynamical degree</term>
                <term xml:lang="en">Toric Geometry</term>
                <term xml:lang="en">Transcendental Number Theory</term>
                <term xml:lang="en">Algebraic dynamics</term>
              </keywords>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>&lt;div&gt;&lt;p&gt;We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a transcendental, non-holonomic function. In the case of toric surfaces, our results are sharp; moreover, we answer a question of Bell by proving that their reductions modulo p are transcendental for all but finitely many prime numbers p.&lt;/p&gt;&lt;/div&gt;</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-193738" status="VALID">
          <idno type="IdRef">111872227</idno>
          <idno type="ISNI">0000000403832988</idno>
          <idno type="RNSR">200511878U</idno>
          <idno type="ROR">https://ror.org/01ekw7f87</idno>
          <orgName>Institut Camille Jordan</orgName>
          <orgName type="acronym">ICJ</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Bât. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-lyon1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-126765" type="direct"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation active="#struct-194495" type="direct"/>
            <relation active="#struct-219748" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-300284" type="direct"/>
            <relation active="#struct-1327915" type="indirect"/>
            <relation name="UMR5208" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-521751" status="VALID">
          <orgName>Combinatoire, théorie des nombres</orgName>
          <orgName type="acronym">CTN</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-lyon1.fr/spip.php?article11</ref>
          </desc>
          <listRelation>
            <relation active="#struct-193738" type="direct"/>
            <relation active="#struct-126765" type="indirect"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation active="#struct-194495" type="indirect"/>
            <relation active="#struct-219748" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-300284" type="indirect"/>
            <relation active="#struct-1327915" type="indirect"/>
            <relation name="UMR5208" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-126765" status="VALID">
          <idno type="ROR">https://ror.org/05s6rge65</idno>
          <orgName>École Centrale de Lyon</orgName>
          <orgName type="acronym">ECL</orgName>
          <desc>
            <address>
              <addrLine>36 avenue Guy de Collongue - 69134 Ecully cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ec-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-219748" status="VALID">
          <idno type="IdRef">052444724</idno>
          <idno type="ISNI">0000 0001 2292 0228</idno>
          <orgName>Institut National des Sciences Appliquées de Lyon</orgName>
          <orgName type="acronym">INSA Lyon</orgName>
          <date type="start">1957-03-18</date>
          <desc>
            <address>
              <addrLine>20 Avenue Albert Einstein, 69621 Villeurbanne cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
            <relation active="#struct-301232" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300284" status="VALID">
          <idno type="IdRef">028209966</idno>
          <idno type="ISNI">0000 0001 2158 1682</idno>
          <idno type="ROR">https://ror.org/04yznqr36</idno>
          <idno type="Wikidata">Q623154</idno>
          <orgName>Université Jean Monnet - Saint-Étienne</orgName>
          <orgName type="acronym">UJM</orgName>
          <date type="start">1969-03-27</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>10, Rue Tréfilerie – CS 8230142023 Saint-Étienne Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-st-etienne.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1327915" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-1327915" status="VALID">
          <idno type="IdRef">285395831</idno>
          <orgName>Université Jean Monnet (EPSCPE)</orgName>
          <orgName type="acronym">UJM EPE</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>10 rue Tréfilerie42100 Saint-Etienne</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-st-etienne.fr/fr/index.html</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>
      </listOrg>
    </back>
  </text>
</TEI>