论文标题
简单产物三角剖分的定向矩阵
Oriented Matroids from Triangulations of Products of Simplices
论文作者
论文摘要
我们从两种简单的产物的三角剖分中引入了定向矩阵的结构。为此，我们使用这种三角剖分的结构在多面体匹配场上。定向的曲霉由在超刺激性的成曲线细分中的细胞上兼容的chirotopes组成，这可能具有独立的关注。特别是，我们使用Matroid语言在Hyperfields上概括了这一点，该语言为在Hyperfields上构建矩阵提供了新的方法。我们工作中的一个反复出现的主题是，可以通过新的配方和证明方法扩展各种热带结构。
We introduce a construction of oriented matroids from a triangulation of a product of two simplices. For this, we use the structure of such a triangulation in terms of polyhedral matching fields. The oriented matroid is composed of compatible chirotopes on the cells in a matroid subdivision of the hypersimplex, which might be of independent interest. In particular, we generalize this using the language of matroids over hyperfields, which gives a new approach to construct matroids over hyperfields. A recurring theme in our work is that various tropical constructions can be extended beyond tropicalization with new formulations and proof methods.
