Odd cycles and a class of facets of the axial 3-index assignment polytope
On a conjecture concerning dyadic oriented matroids.
On a covering problem of Mullin and Stanton for binary matroids.
On a generalization of the matroid
On a unimodality conjecture in matroid theory.
On certain n-connected matroids.
On P-polynomial representations of projective geometries in algebraic combinatorial geometries.
On sets of vectors of a finite vector space in which every subset of basis size is a basis
It is shown that the maximum size of a set of vectors of a -dimensional vector space over , with the property that every subset of size is a basis, is at most , if , and at most , if , where and is prime. Moreover, for , the sets of maximum size are classified, generalising Beniamino Segre’s “arc is a conic” theorem. These results have various implications. One such implication is that a matrix, with and entries from , has columns which are linearly dependent. Another is...
On Squashed Designs.
On Subgraphs as Matroid Cells.
On sums over partially ordered sets.
On the center of the fundamental group of the complement of a hyperplane arrangement.
On the Coordinatization of Oriented Matroids.
On the excluded minors for matroids of branch-width three.
On the local linear independence of translates of a box spline
On the maximum positive semi-definite nullity and the cycle matroid of graphs.
On the notion of transversal of a sum of matroids
On the number of matroids on a finite set.
On the rank of random subsets of finite affine geometry
The aim of the paper is to give an effective formula for the calculation of the probability that a random subset of an affine geometry AG(r-1,q) has rank r. Tables for the probabilities are given for small ranks. The expected time to the first moment at which a random subset of an affine geometry achieves the rank r is derived.
On the Realization of Convex Polytopes, Euler's Formula and Möbius Functions (Short Communication)