Laminar matroids

A laminar family is a collection A of subsets of a set E such that, for any two intersecting sets, one is contained in the other. For a capacity function c on A, let I be {I : |I ∩ A| ≤ c(A) for all A ∈ A}. Then I is the collection of independent sets of a (laminar) matroid on E. We present a method of compacting laminar presentations, characterize the class of laminar matroids by their excluded minors, present a way to construct all laminar matroids using basic operations, and compare the class of laminar matroids to other well-known classes of matroids.