A hereditary class of (finite combinatorial) geometries is a collection of geometries which is closed under taking minors and direct sums. A sequence of universal models for a hereditary class 'S ofâ€¦ (More)

We prove that a binary geometry of rank n {n > 2) not containing M(Ky and F-, (respectively, M(K5) and C10) as a minor has at most 3/i 3 (respectively, 4Â« 5) points. Here, M(K5) is the cycle geometryâ€¦ (More)

Let q be an odd prime power not divisible by 3. In Part I of this series, it was shown that the number of points in a rank-n combinatorial geometry (or simple matroid) representable over GF(3) andâ€¦ (More)

For a minor-closed class M of matroids, we let h(k) denote the maximum number of elements of a simple rank-k matroid in M. We prove that, if M does not contain all simple rank-2 matroids, then h(k)â€¦ (More)

The general concept of a finite Radon transform is due to Ethan Balker [Z]In this paper, we shall discuss some applications to the theory of combinatorial geometries. We should remark here that someâ€¦ (More)