The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings |
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| Authors: | Birkett Huber Jörg Rambau Francisco Santos |
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| Institution: | (1) Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720-5070, USA, e-mail: birk@isc.tamu.edu, US;(2) Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustrasse 7, 14195 Berlin, Germany, e-mail: rambau@zib.de, DE;(3) Depto. de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain, e-mail: santos@matesco.unican.es, ES |
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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.
Received February 18, 1999 / final version received January 25, 2000?Published online May 22, 2000 |
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| Keywords: | Mathematics Subject Classification (1991): 52B11 52B20 14M25 |
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