A matroid-like structure defined on a convex geometry, called a cg-matroid, is defined by S. Fujishige, G. A. Koshevoy, and Y. Sano in [9]. A cg-matroid whose rank function is naturally defined is called a strict cg-matroid. In this paper, we give characterizations of strict cg-matroids by their rank functions.

We prove that a matroid with at least two elements is a tangle matroid if and only if it cannot be covered by three hyperplanes. Some consequences of this theorem are also noted. In particular, no binary matroid of rank at least two is a tangle matroid.

A link between matroid theory and p-branes is discussed. The Schild type action for p-branes and matroid bundle notion provide the two central structures for such a link. We use such a connection to bring the duality concept in matroid theory to p-branes physics. Our analysis may be of particular interest in M-theory and in matroid bundle theory.

In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which described as matroid cryptomorphisms . A q -matroid is -analogue where subspaces play role subsets in theory. this article we establish -matroids. doing so highlight difference between and its -analogue. We introduce comprehensive set axiom show them existing -matroid. These ax...

In this note we introduce a sufficient condition for the OrlikSolomon algebra associated to a matroid M to be l-adic and we prove that this condition is necessary when M is binary (in particular graphic). Moreover, this result cannot be extended to the class of all matroids.

We prove that, for any finite field F and positive integer n; there exists an integer l such that if M is a simple F-representable matroid with no MðKnÞ-minor, then jEðMÞjplrðMÞ: r 2002 Elsevier Science (USA). All rights reserved.

17 graph. The cuts of G are the minimal dependent sets of a matroid T ? (G) on the edge set E. A matroid T is cographic if there exists some graph G such that T is isomorphic to the cut matroid T ? (G). Every cographic matroid is representable over any eld 18]. Therefore if an access structure A has a cographic appropriate matroid, then A is universally ideal. Unlike graphic matroids, we do not...