Asymptotic predominance of sparse paving matroids

Establish whether sparse paving matroids asymptotically predominate among all matroids, in the sense asserted by the longstanding sparse-paving conjecture.

Background

Sparse paving matroids are those matroids that are both paving and copaving. The paper explains that sparse paving matroids form a one-dimensional face of the unlabelled polytope Omega_{r,n}, with only two vertices populated by sparse paving matroids. The asymptotic predominance conjecture is relevant because, if true, it would imply that the number of vertices of Omega_{r,n} is negligible relative to the total number of matroid isomorphism classes, subject to the additional issue of how many sparse paving classes share the same polytope point.