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.

翻译：在两个拟阵中寻找最大基数公共独立集（即拟阵交问题）是经典的组合优化问题，它推广了多个众所周知的难题，例如寻找最大二分图匹配、最大彩色森林以及有向图中的树形图。枚举两个（或多个）拟阵中的所有极大公共独立集是一个经典的枚举问题。本文研究这些问题的“交集”：给定两个拟阵和一个阈值$\tau$，目标是枚举这两个拟阵中所有基数至少为$\tau$的极大公共独立集。我们证明该问题可在多项式延迟和多项式空间内解决。此外，我们还讨论如何按基数非递增顺序枚举两个拟阵的所有极大公共独立集。