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.
Minimal cycle bases of the lexicographic product of graphs
A construction of minimum cycle bases of the lexicographic product of graphs is presented. Moreover, the length of a longest cycle of a minimal cycle basis is determined.
Minimality of toric arrangements
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
Mnëv's universality theorem revisited.
Modular Substructures in Pseudomodular Lattices.
Multimatroids. II: Orthogonality, minors and connectivity.