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

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 A1 + · · ·+Ar of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding C (A1 Ar). In this paper we extend this correspondence in a natural way to cover also noncoherent 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.

4 Figures and Tables

Statistics

05'00'02'04'06'08'10'12'14'16
Citations per Year

51 Citations

Semantic Scholar estimates that this publication has 51 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@inproceedings{Huber1999TheCT, title={The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings}, author={Birkett Huber and J{\"{o}rg Rambau and Francisco Santos}, year={1999} }