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  <doc>
    <id>901</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-03-01</completedDate>
    <publishedDate>2006-03-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Enumeration and Random Realization of Triangulated Surfaces</title>
    <abstract language="eng">We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.</abstract>
    <identifier type="serial">06-07</identifier>
    <identifier type="opus3-id">901</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9012</identifier>
    <enrichment key="SourceTitle">Appeared in: Discrete Differential Geometry (A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, eds.). Oberwolfach Seminars 38, 235-253. Birkhäuser, Basel, 2008</enrichment>
    <author>Frank H. Lutz</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-07</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>triangulated surfaces</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral manifolds</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="52B70">Polyhedral manifolds</collection>
    <collection role="msc" number="57Q15">Triangulating manifolds</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/901/ZR-06-07.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/901/ZR-06-07.ps</file>
  </doc>
  <doc>
    <id>902</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-03-01</completedDate>
    <publishedDate>2006-03-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Triangulated Manifolds with Few Vertices: Combinatorial Manifolds</title>
    <abstract language="eng">In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.</abstract>
    <identifier type="serial">06-08</identifier>
    <identifier type="opus3-id">902</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9028</identifier>
    <author>Frank H. Lutz</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-08</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>triangulated manifolds</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>combinatorial properties</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>minimal triangulations</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="05C30">Enumeration in graph theory</collection>
    <collection role="msc" number="52B05">Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]</collection>
    <collection role="msc" number="52B70">Polyhedral manifolds</collection>
    <collection role="msc" number="57Q15">Triangulating manifolds</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/902/ZR-06-08.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/902/ZR-06-08.ps</file>
  </doc>
  <doc>
    <id>905</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-03-02</completedDate>
    <publishedDate>2006-03-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyhedra of Genus 2 with 10 Vertices and Minimal Coordinates</title>
    <abstract language="eng">We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.</abstract>
    <identifier type="serial">06-12</identifier>
    <identifier type="opus3-id">906</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9054</identifier>
    <enrichment key="SourceTitle">Appeared in: Electronic Geometry Models, No. 2005.08.001 (2007). http://www.eg-models.de/2005.08.001/</enrichment>
    <author>Stefan Hougardy</author>
    <author>Frank H. Lutz</author>
    <author>Mariano Zelke</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-12</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>triangulated surfaces</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>minimal triangulations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral realizations</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="52B70">Polyhedral manifolds</collection>
    <collection role="msc" number="57Q15">Triangulating manifolds</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/905/ZR-06-12.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/905/ZR-06-12.ps</file>
  </doc>
  <doc>
    <id>906</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-03-02</completedDate>
    <publishedDate>2006-03-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyhedra of Genus 3 with 10 Vertices and Minimal Coordinates</title>
    <abstract language="eng">We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.</abstract>
    <identifier type="serial">06-13</identifier>
    <identifier type="opus3-id">907</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9064</identifier>
    <enrichment key="SourceTitle">Appeared in: Electronic Geometry Models, No. 2006.02.001 (2007). http://www.eg-models.de/2006.02.001/</enrichment>
    <author>Stefan Hougardy</author>
    <author>Frank H. Lutz</author>
    <author>Mariano Zelke</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>triangulated surfaces</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>minimal triangulations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral realizations</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="52B70">Polyhedral manifolds</collection>
    <collection role="msc" number="57Q15">Triangulating manifolds</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/906/ZR-06-13.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/906/ZR-06-13.ps</file>
  </doc>
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