Equitable Matroids

One way to choose a basis of a matroid at random is to choose an ordering of the ground set uniformly at random and then use the greedy algorithm to find a basis. We investigate the class of matroids having the property that this procedure yields a basis uniformly at random. We show how this class is related to some other naturally-defined families of matroids and consider how it behaves under well-known matroid operations.