TY - GEN A1 - Huber, Birkett A1 - Rambau, Jörg A1 - Santos, Francisco T1 - The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings N2 - 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. T3 - ZIB-Report - SC-98-44 KW - Polyhedral subdivision KW - fiber polytope KW - mixed subdivision KW - lifting subdivision KW - Minkowski sum KW - Cayley Trick KW - Bohne-Dress Theorem Y1 - 1999 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/387 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-3874 ER -