论文标题
分区和一般无限曲霉的交点
Intersection of a partitional and a general infinite matroid
论文作者
论文摘要
让$ e $成为可能的无限套件，让$ m $和$ n $是$ e $定义的Matroids。我们说，如果$ m $和$ n $共享一对$ \ {m，n \} $具有相交属性，则是独立的套装$ i $ cunding a tepartition $ i_m \ sqcup i_n $，这样，$ \ mathsf {spansf {span} _m（i_m（i_m）_m（i_m）纳什·威廉姆斯（Nash-Williams）的矩形交点猜想表明，每个矩形对具有相交特性。 在一个矩形均匀的情况下，鲍勒和卡梅尔辛表明，猜想是已知且易于证明的，其特殊情况下暗示了猜想是构造的，其中一种矩形是均匀的基质体的直接总和，即partitional Matroid。我们表明，如果$ m $是任意的矩阵，而$ n $是有限的许多统一矩形的直接总和，则$ \ {m，n \} $具有交叉点属性。
Let $ E $ be a possibly infinite set and let $ M $ and $ N $ be matroids defined on $ E $. We say that the pair $ \{ M,N \} $ has the Intersection property if $ M $ and $ N $ share an independent set $ I $ admitting a bipartition $ I_M\sqcup I_N $ such that $ \mathsf{span}_M(I_M)\cup \mathsf{span}_N(I_N)=E $. The Matroid Intersection Conjecture of Nash-Williams says that every matroid pair has the Intersection property. The conjecture is known and easy to prove in the case when one of the matroids is uniform and it was shown by Bowler and Carmesin that the conjecture is implied by its special case where one of the matroids is a direct sum of uniform matroids, i.e., is a partitional matroid. We show that if $ M $ is an arbitrary matroid and $ N $ is the direct sum of finitely many uniform matroids, then $ \{ M, N \} $ has the Intersection property.
