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    <id>371</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
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    <completedDate>1998-11-02</completedDate>
    <publishedDate>1998-11-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A counterexample to an integer analogue of Caratheodorys theorem</title>
    <abstract language="eng">For $n\geq 6$ we provide a counterexample to the conjecture that every integral vector of a $n$-dimensional integral polyhedral pointed cone $C$ can be written as a nonnegative integral combination of at most $n$ elements of the Hilbert basis of $C$. In fact, we show that in general at least $\lfloor 7/6 \cdot n \rfloor$ elements of the Hilbert basis are needed.</abstract>
    <identifier type="serial">SC-98-28</identifier>
    <identifier type="opus3-id">372</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3718</identifier>
    <enrichment key="SourceTitle">Appeared in: Journal für die Reine und Angewandte Mathematik 510, 1999, pp. 179-185</enrichment>
    <author>Winfried Bruns</author>
    <author>Joseph Gubeladze</author>
    <author>Martin Henk</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-28</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integral pointed cones</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hilbert basis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integral Carathéodory property</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/371/SC-98-28.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/371/SC-98-28.pdf</file>
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