Sparse paving matroid predominance

Establish whether sparse paving matroids asymptotically predominate among all matroids.

Background

Sparse paving matroids form a distinguished one-dimensional face of the polytope \Omega_{r,n}, and the paper discusses their possible asymptotic dominance among all matroids. The stated conjecture originates with Crapo and Rota and is cited as a longstanding unresolved assertion; more precise formulations are referenced in the literature.

References

A famous conjecture, originating from a hypothesis by Crapo and Rota in p.~317, asserts that asymptotically almost all matroids are sparse paving.

— The polytope of all matroids  (2502.20157 - Ferroni et al., 27 Feb 2025) in Section 5, subsection “Split matroids and their subclasses”; reiterated in Section 6.1