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

Birkett Huber; Jörg Rambau; Francisco Santos

Journal of the European Mathematical Society (2000)

- Volume: 002, Issue: 2, page 179-198
- ISSN: 1435-9855

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topHuber, 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 -

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