On the refinements of a polyhedral subdivision.

@article{Santos2001,
abstract = {Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced subdivision. In particular, we define the refinement polytope associated to any pi-induced subdivision S, which is a generalization of the fiber polytope and shares most of its properties. As applications to the theory we prove that if a point configuration has non-regular subdivisions then it has non-regular triangulations and we provide simple proofs of the existence of non-regular subdivisions for many particular point configurations.},
author = {Santos, Francisco},
journal = {Collectanea Mathematica},
keywords = {Geometría proyectiva; Politopos; Refinamiento; Poliedro; refinement polytope; fiber polytope; polyhedral subdivision; Baues conjecture},
language = {eng},
number = {3},
pages = {231-256},
title = {On the refinements of a polyhedral subdivision.},
url = {http://eudml.org/doc/42771},
volume = {52},
year = {2001},
}

TY - JOUR
AU - Santos, Francisco
TI - On the refinements of a polyhedral subdivision.
JO - Collectanea Mathematica
PY - 2001
VL - 52
IS - 3
SP - 231
EP - 256
AB - Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced subdivision. In particular, we define the refinement polytope associated to any pi-induced subdivision S, which is a generalization of the fiber polytope and shares most of its properties. As applications to the theory we prove that if a point configuration has non-regular subdivisions then it has non-regular triangulations and we provide simple proofs of the existence of non-regular subdivisions for many particular point configurations.
LA - eng
KW - Geometría proyectiva; Politopos; Refinamiento; Poliedro; refinement polytope; fiber polytope; polyhedral subdivision; Baues conjecture
UR - http://eudml.org/doc/42771
ER -