Oriented Lagrangian Matroids

Oriented Lagrangian Matroids

The aim of this paper is to develop, by analogy with the theory of oriented (ordinary) matroids [2], an oriented version of the theory of Lagrangian symplectic matroids [7]. Recall that the concept of an oriented matroid axiomatises, in combinatorial form, the properties of the ensemble of non-zero k× k minors of a real k× n matrix A, say. The k-subsets of indices of columns of A such that the ...

Fachbereich 3 Mathematik Oriented Matroids Oriented Matroids

Lagrangian Matroids and Cohomology

We prove that ∆-matroids associated with maps on compact closed surfaces are representable, with the space of representation provided by cohomology of the surface with punctured points.

Lagrangian pairs and Lagrangian orthogonal matroids

Represented Coxeter matroids of types Cn and Dn, that is, symplectic and orthogonal matroids arising from totally isotropic subspaces of symplectic or (even-dimensional) orthogonal spaces, may also be represented in buildings of type Cn and Dn, respectively (see [4, Chapter 7]). Indeed, the particular buildings involved are those arising from the flags or oriflammes, respectively, of totally is...

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...