论文标题
定向矩阵的varchenko决定因素
The Varchenko Determinant of an Oriented Matroid
论文作者
论文摘要
Varchenko于1993年推出了超平面布置室的距离功能，这引起了决定因素，其在位置$（c，d）$的条目是Chambers $ C $和$ d $之间的距离，并计算出该决定因素。 2017年，Aguiar和Mahajan提供了该距离函数的概括，并计算了相应的决定因素。本文将其距离函数扩展到定向的矩阵的顶部，并计算这样定义的决定因素。定向的基型具有不错的特性，可以是某些数学结构的抽象，包括超平面和球体排列，多型，有向图甚至分子化学中的手性。 Hochstättler和Welker独立并采用了另一种方法，在2019年也计算出同样的决定因素。
Varchenko introduced in 1993 a distance function on the chambers of a hyperplane arrangement that gave rise to a determinant whose entry in position $(C, D)$ is the distance between the chambers $C$ and $D$, and computed that determinant. In 2017, Aguiar and Mahajan provided a generalization of that distance function, and computed the corresponding determinant. This article extends their distance function to the topes of an oriented matroid, and computes the determinant thus defined. Oriented matroids have the nice property to be abstractions of some mathematical structures including hyperplane and sphere arrangements, polytopes, directed graphs, and even chirality in molecular chemistry. Independently and with another method, Hochstättler and Welker also computed in 2019 the same determinant.
