Patchworking oriented matroids

Fachbereich 3 Mathematik Oriented Matroids Oriented Matroids

Oriented Matroids

The theory of oriented matroids provides a broad setting in which to model, describe, and analyze combinatorial properties of geometric configurations. Apparently totally different mathematical objects such as point and vector configurations, arrangements of hyperplanes, convex polytopes, directed graphs, and linear programs find a common generalization in the language of oriented matroids. The...

Shellability of Oriented Matroids

In Man82] A. Mandel proved that the maximal cells of an Oriented Matroid poset are B-shellable. Our result shows that the whole Oriented Matroid is shellable, too.

Oriented Matroids Today

This dynamic survey offers an “entry point” for current research in oriented matroids. For this, it provides updates on the 1993 monograph “Oriented Matroids” by Björner, Las Vergnas, Sturmfels, White & Ziegler [73], in three parts: 1. a sketch of a few “Frontiers of Research” in oriented matroid theory, 2. an update of corrections, comments and progress as compared to [73], and 3. an extensive...

Triangulations of Oriented Matroids

We consider the concept of triangulation of an oriented matroid. We provide a de nition 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 matroidM and extensions of its dualM , via the so-called lift...