论文标题
面向拼凑的矩形
Patchworking Oriented Matroids
论文作者
论文摘要
在先前的工作中，我们通过两种简单的产物进行了三角剖分，对（不一定可以实现的）构造了（不一定可以实现的）构造。在此后续纸中，我们使用Viro拼凑而成的变体来从三角剖分的多面体结构中得出定向的矩阵的拓扑表示，因此除了热带代数几何形状外，还找到了拼打的组合表现。我们通过将拼凑而成的过程作为受控的细胞合并过程来实现这一目标，并以热带为导向的矩阵的结构为指导。一个关键的见解是一种新的有前途的技术，可以表明最终的细胞复合体是常规的。
In a previous work, we gave a construction of (not necessarily realizable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a variant of Viro's patchworking to derive a topological representation of the oriented matroid directly from the polyhedral structure of the triangulation, hence finding a combinatorial manifestation of patchworking besides tropical algebraic geometry. We achieve this by rephrasing the patchworking procedure as a controlled cell merging process, guided by the structure of tropical oriented matroids. A key insight is a new promising technique to show that the final cell complex is regular.
