Random packing by matroid bases and triangles (Q1901027)

A matroid \(M\) on the set \(E\) is said to be packable by bases if \(E\) is the disjoint union of bases of \(M\). It is randomly packable by bases if every collection of pairwise disjoint bases may be extended to a disjoint collection with \(E\) as its union. This paper is devoted to exploring packability by bases and other structures and includes results like the following theorem. Let \(M\) be a connected matroid having rank \(r\). If \(M\) is randomly packable by bases, then \(M\) is identically self-dual or isomorphic to \(\mathbb{U}_{r, kr}\) for some positive integer \(k\).