Lectures on matroids

Lectures

On cographic matroids and signed-graphic matroids

We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph Σ iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that Σ must be the projective-planar dual signed graph of an actual imbedding of G in the projective plane. As a corollary we get that, if G1, . . . , G29 denote the 29 nonseparable forbidden minors for projective-pl...

Matroids on convex geometries (cg-matroids)

We consider matroidal structures on convex geometries, which we call cg-matroids. The concept of a cg-matroid is closely related to but different from that of a supermatroid introduced by Dunstan, Ingleton, and Welsh in 1972. Distributive supermatroids or poset matroids are supermatroids defined on distributive lattices or sets of order ideals of posets. The class of cg-matroids includes distri...

CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS

The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simul...

On Pseudomodular Matroids and Adjoints on Pseudomodular Matroids and Adjoints

1992 Mathematisches Institut Universitt at zu KK oln Weyertal 86-90 D{5000 KK oln 41 (Lindenthal) Germany Telefon (0221) 470{3937 Telex 8882291 unik d Telefax (0221) 470{5160 Abstract There are two concepts of duality in combinatorial geometry. A set theoretical one, generalizing the structure of two orthocomplementary vector spaces and a lattice theoretical concept of an adjoint, that mimics d...