Triangulations Of Oriented Matroids
Download Triangulations Of Oriented Matroids PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Triangulations Of Oriented Matroids book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Triangulations of Oriented Matroids
The author considers the concept of triangulation of an oriented matroid. He provides a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M} DEGREES*$, via the so-called lifting triangulations is studied, showing that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of pol
Triangulations of Oriented Matroids
Author: Francisco Santos
language: en
Publisher: American Mathematical Soc.
Release Date: 2002
We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.
Circuit Admissible Triangulations of Oriented Matroids
Abstract: "All triangulations of euclidean oriented matroids are of the same PL-homeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PL-spheres. For non-euclidean oriented matroids this question is wide open. One key point in the proof of Anderson is the following fact: for every triangulation of a euclidean oriented matroid the adjacency graph of the set of all simplices 'intersecting' a segment [p-p+] is a path. We call this graph the [p-p+]-adjacency graph of the triangulation. While we cannot solve the problem of the topological type of triangulations of general oriented matroids we show in this note that for every circuit admissible triangulation of an arbitrary oriented matroid the [p-p+] adjacency graph is path."