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    <id>154</id>
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    <language>eng</language>
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    <completedDate>1994-10-17</completedDate>
    <publishedDate>1994-10-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Gröbner bases of lattices, corner polyhedra, and integer programming</title>
    <abstract language="eng">We investigate the generating sets (``Gröbner bases'') of integer lattices which correspond to the Gröbner bases of the associated binomial ideals. Extending results in Sturmfels and Thomas, preprint 1994, we obtain a geometric characterization of the universal Gröbner basis in terms of the vertices and edges of the associated corner polyhedra. We emphasize the special case where the lattice has finite index. In this case the corner polyhedra were studied by Gomory, and there is a close connection to the ``group problem in integer programming'' Schrijver, p.~363. We present exponential lower and upper bounds for the size of a reduced Gröbner basis. The initial complex of (the ideal of) a lattice is shown to be dual to the boundary of a certain simple polyhedron.</abstract>
    <identifier type="serial">SC-94-26</identifier>
    <identifier type="opus3-id">154</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1548</identifier>
    <enrichment key="SourceTitle">Appeared in: Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry 36 (1995) pp. 282-298</enrichment>
    <author>Bernd Sturmfels</author>
    <author>Robert Weismantel</author>
    <author>Günter M. Ziegler</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-94-26</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/154/SC-94-26.ps</file>
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