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  <doc>
    <id>386</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-01-27</completedDate>
    <publishedDate>1999-01-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Generalized Baues Problem for Cyclic Polytopes II</title>
    <abstract language="eng">Given an affine surjection of polytopes $\pi: P \to Q$, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of $Q$ which are induced by the map $\pi$ has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes $\pi: C(n,d') \to C(n,d)$ for all $1 \leq d &lt; d' &lt; n$.</abstract>
    <identifier type="serial">SC-98-43</identifier>
    <identifier type="opus3-id">387</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3862</identifier>
    <enrichment key="SourceTitle">Appeared in: Publications de l'Institut Mathematique, Belgrade 66 (1999) 3-15</enrichment>
    <author>Christos A. Athanasiadis</author>
    <author>Jörg Rambau</author>
    <author>Francisco Santos</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-43</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Generalized Baues Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Polyhedral Subdivisions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Induced Subdivisions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Poset</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Spherical</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cyclic Polytopes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bistellar Operations</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="52B99">None of the above, but in this section</collection>
    <collection role="msc" number="52C22">Tilings in n dimensions [See also 05B45, 51M20]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="ZIB-PolSub">ZIB-PolSub</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/386/SC-98-43.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/386/SC-98-43.pdf</file>
  </doc>
  <doc>
    <id>387</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-01-28</completedDate>
    <publishedDate>1999-01-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings</title>
    <abstract language="eng">In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of \emph{coherent} mixed subdivisions of a Minkowski sum $\mathcal{A}_1+\cdots+\mathcal{A}_r$ of point configurations and of \emph{coherent} polyhedral subdivisions of the associated Cayley embedding $\mathcal{C}(\mathcal{A}_1,\dots,\mathcal{A}_r)$. In this paper we extend this correspondence in a natural way to cover also \emph{non-coherent} subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions of Lawrence polytopes provides a new independent proof of the Bohne-Dress Theorem on zonotopal tilings. This application uses a combinatorial characterization of lifting subdivisions, also originally proved by Santos.</abstract>
    <identifier type="serial">SC-98-44</identifier>
    <identifier type="opus3-id">388</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3874</identifier>
    <enrichment key="SourceTitle">Appeared in: "The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings", Journal of the European Mathematical Society, 2 (2000) 179-198</enrichment>
    <author>Birkett Huber</author>
    <author>Jörg Rambau</author>
    <author>Francisco Santos</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Polyhedral subdivision</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>fiber polytope</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mixed subdivision</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>lifting subdivision</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Minkowski sum</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cayley Trick</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bohne-Dress Theorem</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="14M25">Toric varieties, Newton polyhedra [See also 52B20]</collection>
    <collection role="msc" number="52B11">n-dimensional polytopes</collection>
    <collection role="msc" number="52B20">Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="ZIB-PolSub">ZIB-PolSub</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/387/SC-98-44.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/387/SC-98-44.pdf</file>
  </doc>
  <doc>
    <id>357</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1998-05-06</completedDate>
    <publishedDate>1998-05-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Generalized Baues Problem for Cyclic Polytopes I.</title>
    <abstract language="eng">The Generalized Baues Problem asks whether for a given point configuration the order complex of all its proper polyhedral subdivisions, partially ordered by refinement, is homotopy equivalent to a sphere. In this paper, an affirmative answer is given for the vertex sets of cyclic polytopes in all dimensions. This yields the first non-trivial class of point configurations with neither a bound on the dimension, the codimension, nor the number of vertice for which this is known to be true. Moreover, it is shown that all triangulations of cyclic polytopes are lifting triangulations. This contrasts the fact that in general there are many non-regular triangulations of cyclic polytopes. Beyond this, we find triangulations of $C(11,5)$ with flip deficiency. This proves---among other things---that there are triangulations of cyclic polytopes that are non-regular for every choice of points on the moment curve.</abstract>
    <identifier type="serial">SC-98-14</identifier>
    <identifier type="opus3-id">358</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3579</identifier>
    <enrichment key="SourceTitle">Appeared in: European Journal of Combinatorics, 21(1), 2000, 65-83</enrichment>
    <author>Jörg Rambau</author>
    <author>Francisco Santos</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-14</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Generalized Baues Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Polyhedral Subdivisions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Induced Subdivisions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Poset</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Spherical</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cyclic Polytopes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bistellar Operations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Flip Defici</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="52B99">None of the above, but in this section</collection>
    <collection role="msc" number="52C22">Tilings in n dimensions [See also 05B45, 51M20]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="ZIB-PolSub">ZIB-PolSub</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/357/SC-98-14.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/357/SC-98-14.pdf</file>
  </doc>
</export-example>
