ON MATROIDS AND LINEARLY INDEPENDENT SET FAMILIES

An Independent Set Axiomatization of Symplectic Matroids

A constrained independent set problem for matroids

In this note, we study a constrained independent set problem for matroids and certain generalizations. The basic problem can be regarded as an ordered version of the matroid parity problem. By a reduction of this problem to matroid intersection, we prove a min-max formula. Studying the weighted case and a delta-matroid generalization, we prove that some of them are not more complex than matroid...

Families of Regular Matroids

This is an introductory paper about the category of regular oriented matroids (ROMs). We compare the homotopy types of the categories of regular and binary matroids. For example, in the unoriented case, they have the same fundamental group but we show that the higher homotopy groups are different for rank three regular and binary matroids. We also speculate on the possible impact of a recent th...

Uniform Families and Count Matroids

On Cancellative Set Families

A family of subsets of an n-set is 2-cancellative if for every four-tuple {A, B, C, D} of its members A ∪B ∪C = A ∪B ∪D implies C = D. This generalizes the concept of cancellative set families, defined by the property that A ∪B 6= A ∪C for A, B, C all different. The asymptotics of the maximum size of cancellative families of subsets of an n-set is known, (Tolhuizen [7]). We provide a new upper ...