论文标题
热带国旗品种
Tropical flag varieties
论文作者
论文摘要
FLAG Matroids是线性子空间标志的组合抽象，就像矩阵是线性子空间一样。我们将旗杆作为部分国旗品种的热带类似物介绍，并证明：（a）旗杆上的点之间的对应关系，（b）有价值的旗帜矩形，（c）投影性热带线性空间的旗帜，（c）（c）（c）（d）连贯的旗帜马特罗德·马特罗德分子。我们介绍和表征投影性热带线性空间，这是我们证明的基本工具。我们将信件应用来证明，地面设置为5尺寸的所有有价值的标志矩形都是可实现的，并举例说明这是6个元素上的flag Matroid失败的示例。
Flag matroids are combinatorial abstractions of flags of linear subspaces, just as matroids are of linear subspaces. We introduce the flag Dressian as a tropical analogue of the partial flag variety, and prove a correspondence between: (a) points on the flag Dressian, (b) valuated flag matroids, (c) flags of projective tropical linear spaces, and (d) coherent flag matroidal subdivisions. We introduce and characterize projective tropical linear spaces, which serve as a fundamental tool in our proof. We apply the correspondence to prove that all valuated flag matroids on ground set up to size 5 are realizable, and give an example where this fails for a flag matroid on 6 elements.
