论文标题
分裂原子体的超图表表征
Hypergraph characterization of split matroids
论文作者
论文摘要
我们提供了一项分裂曲霉的组合研究，该类别是由从热带几何学角度研究的曲霉多型研究所激发的。分裂矩阵的一个不错的特征是它们概括了铺路矩阵，同时在双重性下关闭并带上未成年人。此外，这些矩形被证明可用于为盛装式的尺寸提供精确的渐近界限，并且也暗示了热带草个者的射线的新结果。 在本文中，我们介绍了基本分裂曲霉的概念，这是一个包含所有连接的分型矩阵的分裂矩阵的子类。我们从独立集的角度给出了基本分型矩阵的超图表，并表明所提出的类不仅在二元性和带走未成年人的情况下是关闭的，而且还截断了。我们进一步表明，与分裂的矩形相比，所提出的类可以以单个禁止的未成年人为特征。作为一个应用程序，我们提供了二进制拆分矩阵的完整列表。
We provide a combinatorial study of split matroids, a class that was motivated by the study of matroid polytopes from a tropical geometry point of view. A nice feature of split matroids is that they generalize paving matroids, while being closed under duality and taking minors. Furthermore, these matroids proved to be useful in giving exact asymptotic bounds for the dimension of the Dressian, and also implied new results on the rays of the tropical Grassmannians. In the present paper, we introduce the notion of elementary split matroids, a subclass of split matroids that contains all connected split matroids. We give a hypergraph characterization of elementary split matroids in terms of independent sets, and show that the proposed class is closed not only under duality and taking minors but also truncation. We further show that, in contrast to split matroids, the proposed class can be characterized by a single forbidden minor. As an application, we provide a complete list of binary split matroids.
