Symmetry and Positive Definiteness in Oriented Matroids

Symmetry, oriented matroids and two conjectures of Michel Las Vergnas

The paper has two parts. In the first part we survey the existing results on the cube conjecture of Las Vergnas. This conjecture claims that the orientation of the matroid of the cube is determined by the symmetries of the underlying matroid. The second part deals with euclidean representations of matroids as geometric simplicial complexes defined by symmetry properties abstracting those of zon...

Fachbereich 3 Mathematik Oriented Matroids Oriented Matroids

Extending Positive Definiteness

The main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of ∗-semigroups to positive definite ones. By specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems, like complex, two-sided complex and multidimensional trigonometric moment pr...

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...