Hyperplane Arrangements with a Lattice of Regions.
Independence structures in the geometry of orders.
Inequalities of Bonferroni-Galambos type with applications to the Tutte polynomial and the chromatic polynomial.
Intersection lattices and topological structures of complements of arrangements in
La structure de certains problèmes d'affectation
Landau's and Rado's theorems and partial tournaments.
Les arrangements d'hyperplans : un chapitre de géométrie combinatoire
Linear independences in bottleneck algebra and their coherences with matroids.
Linear programming duality and morphisms
In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....
Local equivalence of transversals in matroids.
MacWilliams identities and matroid polynomials.
Matroid automorphisms of the root system.
Matroid inequalities from electrical network theory.
Matroid polytopes, nested sets and Bergman fans.
Matroidal decomposition of a graph
Matroids describing Bruhat cells.
Matroids in terms of Cayley graphs and some related results.
Matroids over a ring
We introduce the notion of a matroid over a commutative ring , assigning to every subset of the ground set an -module according to some axioms. When is a field, we recover matroids. When , and when is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, i.e. tropical linear spaces, respectively. More generally, whenever is a Dedekind domain, we extend all the usual properties and operations holding for matroids (e.g., duality), and...
Matroids with Sylvester Property.
Maximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem---with an application to graph coloring.