Completeness in 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...

Flows in Oriented Matroids

Recently Hochstättler and Nešetřil [3] introduced the flow lattice of an oriented matroid as generalization of the lattice of all integer flows of a digraph or more general a regular matroid. This lattice is defined as the integer hull of the characteristic vectors of signed circuits. We describe the structure and the dimension of the flow lattice for uniform and rank 3 oriented matroids and co...

Games in Oriented Matroids

We introduce a combinatorial abstraction of two person finite games in an oriented matroid. We also define a combinatorial version of Nash equilibrium and prove that an odd number of equilibria exists. The proof is a purely combinatorial rendition of the Lemke-Howson algorithm.

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.