  Finding a maximum cardinality common independent set in two matroids (also
known as Matroid Intersection) is a classical combinatorial optimization
problem, which generalizes several well-known problems, such as finding a
maximum bipartite matching, a maximum colorful forest, and an arborescence in
directed graphs. Enumerating all maximal common independent sets in two (or
more) matroids is a classical enumeration problem. In this paper, we address an
``intersection'' of these problems: Given two matroids and a threshold $\tau$,
the goal is to enumerate all maximal common independent sets in the matroids
with cardinality at least $\tau$. We show that this problem can be solved in
polynomial delay and polynomial space. We also discuss how to enumerate all
maximal common independent sets of two matroids in non-increasing order of
their cardinalities.

Combinatorics;Data Structures and Algorithms