标题： 拟阵交集和无限拟阵的基打包与覆盖 显示英文标题

标题： Matroid intersection and base packing and covering for infinite matroids

摘要： 我们证明了无限拟阵交猜想与其他几个在无限拟阵理论中出乎意料的不同部分的新猜想是等价的，包括一个基集配对猜想、一个基集覆盖猜想以及一个结合这两个猜想的猜想。 对于有限拟阵，这些等价关系为对应这些猜想的有限定理提供了新的且更简单的证明。 这种新的观点也使我们能够简化对交猜想已知成立的特殊情况的描述，甚至可以稍微扩展这些结果。 显示英文摘要

摘要： We prove that the infinite matroid Intersection Conjecture is equivalent to several other new conjectures in unexpectedly different parts of infinite matroid theory, including a base packing conjecture, a base covering conjecture and a conjecture combining these two. For finite matroids, these equivalences give new and simpler proofs for the finite theorems corresponding to these conjectures. This new point of view also allows us to give a simplified account of the special cases where the intersection conjecture is known to be true and even to extend the results a little bit.