论文标题
基础标志多层药物
Underlying Flag Polymatroids
论文作者
论文摘要
我们通过将贪婪算法的几何形状与单调路径多面体相关联，描述了矩形和基础标志基矩形之间的自然几何关系。这种观点使我们能够将基础标志矩阵的构建概括为多功能。我们表明，通过证明它们通常等效于某些巢穴，与基础标志多膜化的多型聚合物相关。我们用它来表明，子空间安排实现的多符合性可以产生旗帜品种中光滑的旋转品种，并且我们用复曲面的商来解释我们的构造。我们提供了各种示例，这些例子说明了国旗多肌体的丰富组合结构。最后，我们研究了与某些年轻tableaux的枚举有关的多膜型多型的一般单调路径。
We describe a natural geometric relationship between matroids and underlying flag matroids by relating the geometry of the greedy algorithm to monotone path polytopes. This perspective allows us to generalize the construction of underlying flag matroids to polymatroids. We show that the polytopes associated to underlying flag polymatroid are simple by proving that they are normally equivalent to certain nestohedra. We use this to show that polymatroids realized by subspace arrangements give rise to smooth toric varieties in flag varieties and we interpret our construction in terms of toric quotients. We give various examples that illustrate the rich combinatorial structure of flag polymatroids. Finally, we study general monotone paths on polymatroid polytopes, that relate to the enumeration of certain Young tableaux.
