Journal of the European Mathematical Society

, Volume 2, Issue 2, pp 179–198

The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings

  • Birkett Huber
  • Jörg Rambau
  • Francisco Santos
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Abstract.

In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum ?1+...+?r of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding ?(?1,...,?r). In this paper we extend this correspondence in a natural way to cover also 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.

Mathematics Subject Classification (1991): 52B11, 52B20, 14M25 

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Copyright information

© Springer-Verlag Berlin Heidelberg & EMS 2000

Authors and Affiliations

  • Birkett Huber
    • 1
  • Jörg Rambau
    • 2
  • Francisco Santos
    • 3
  1. 1.Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720-5070, USA, e-mail: birk@isc.tamu.eduUS
  2. 2.Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustrasse 7, 14195 Berlin, Germany, e-mail: rambau@zib.deDE
  3. 3.Depto. de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain, e-mail: santos@matesco.unican.esES

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