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

Huber, Birkett, Rambau, Jörg, and Santos, Francisco. "The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings." Journal of the European Mathematical Society 002.2 (2000): 179-198. <http://eudml.org/doc/277752>.

@article{Huber2000,
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 $\mathcal \{A\}_1+\dots +\mathcal \{A\}_r$ of point configurations and of 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 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.},
author = {Huber, Birkett, Rambau, Jörg, Santos, Francisco},
journal = {Journal of the European Mathematical Society},
keywords = {Cayley Trick of elimination theory; Cayley embedding; Lawrence polytope; Bohne-Dress theorem; zonotopal tilings; polytopes; subdivision; zonotopal tiling},
language = {eng},
number = {2},
pages = {179-198},
publisher = {European Mathematical Society Publishing House},
title = {The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings},
url = {http://eudml.org/doc/277752},
volume = {002},
year = {2000},
}

TY - JOUR
AU - Huber, Birkett
AU - Rambau, Jörg
AU - Santos, Francisco
TI - The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
JO - Journal of the European Mathematical Society
PY - 2000
PB - European Mathematical Society Publishing House
VL - 002
IS - 2
SP - 179
EP - 198
AB - 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 $\mathcal {A}_1+\dots +\mathcal {A}_r$ of point configurations and of 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 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.
LA - eng
KW - Cayley Trick of elimination theory; Cayley embedding; Lawrence polytope; Bohne-Dress theorem; zonotopal tilings; polytopes; subdivision; zonotopal tiling
UR - http://eudml.org/doc/277752
ER -