1. Introdu tion Many di erent topi s in mathemati s, ranging from applied subje ts su h as optimization to pure areas su h as arrangements of hyperplanes, naturally lead to matroids. The approa h we will explore is matroid theory as an abstra tion of aÆne and proje tive geometry. Therefore the rst several se tions will survey some elementary, although perhaps unfamiliar, aspe ts of geometry. We...

This paper surveys recent work that is aimed at generalising the results and techniques of the Graph Minors Project of Robertson and Seymour to matroids. For Dominic Welsh, on the occasion of his retirement.

In 1981, Stanley applied the Aleksandrov–Fenchel Inequalities to prove a logarithmic concavity theorem for regular matroids. Using ideas from electrical network theory we prove a generalization of this for the wider class of matroids with the “half–plane property”. Then we explore a nest of inequalities for weighted basis– generating polynomials that are related to these ideas. As a first resul...

We claim that M(atroid) theory may provide a mathematical framework for an underlying description of M-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas property plays a central role in our formalism. We outline how this definition may be carried over M-theory. As a consequence of our analysis we find a new type of act...

ing from the behavior of linearly independent sets of columns of a matrix, in 1935, Whitney defined a matroid M to consist of a finite set E (or E(M)) and a collection I (or I(M)) of subsets of E called independent sets with the properties that the empty set is independent; every subset of an independent set is independent; and if one independent set has more elements than another, then an elem...