The Cayley Trick, lifting subdivisions and the Bohne–Dress theorem on zonotopal tilings
Journal of the European Mathematical Society, Tome 2 (2000) no. 2, pp. 179-198
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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(A,...,Ar). 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.
@article{JEMS_2000_2_2_a2,
author = {Birkett Huber and J\"org Rambau and Francisco Santos},
title = {The {Cayley} {Trick,} lifting subdivisions and the {Bohne{\textendash}Dress} theorem on zonotopal tilings},
journal = {Journal of the European Mathematical Society},
pages = {179--198},
publisher = {mathdoc},
volume = {2},
number = {2},
year = {2000},
doi = {10.1007/s100970050003},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970050003/}
}
TY - JOUR AU - Birkett Huber AU - Jörg Rambau AU - Francisco Santos TI - The Cayley Trick, lifting subdivisions and the Bohne–Dress theorem on zonotopal tilings JO - Journal of the European Mathematical Society PY - 2000 SP - 179 EP - 198 VL - 2 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1007/s100970050003/ DO - 10.1007/s100970050003 ID - JEMS_2000_2_2_a2 ER -
%0 Journal Article %A Birkett Huber %A Jörg Rambau %A Francisco Santos %T The Cayley Trick, lifting subdivisions and the Bohne–Dress theorem on zonotopal tilings %J Journal of the European Mathematical Society %D 2000 %P 179-198 %V 2 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1007/s100970050003/ %R 10.1007/s100970050003 %F JEMS_2000_2_2_a2
Birkett Huber; Jörg Rambau; Francisco Santos. The Cayley Trick, lifting subdivisions and the Bohne–Dress theorem on zonotopal tilings. Journal of the European Mathematical Society, Tome 2 (2000) no. 2, pp. 179-198. doi: 10.1007/s100970050003
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