论文标题
关于某种类型的超平面布置的枚举
On the Enumeration of a Certain Type of Hyperplane Arrangements
论文作者
论文摘要
在本文中，我们在主要定理中证明，一方面某种类型的真实超平面布置的同构类别与相关判别式排列的凸锥的同构类别之间存在两者。考虑的超平面布置和同构类别的类型已精确定义。结果，我们通过计算判别安排的特征多项式来列举这种同构类别。在一定的限制下，列举值被证明与判别排列无关。后来，我们观察到我们对超平面布置类型的限制是一种轻度的限制，并且这种有条件的限制是相当通用的。此外，限制是根据普通系统无并发状态定义的，这是一种通用条件。我们还讨论了正常系统的两个示例，这些示例在最后一节中并非无异常，并列举了同构类别的数量。
In this article we prove in the main theorem that, there is a bijection between the isomorphism classes of a certain type of real hyperplane arrangements on the one hand, and the antipodal pairs of convex cones of an associated discriminantal arrangement on the other hand. The type of hyperplane arrangements considered and the isomorphism classes have been defined precisely. As a consequence we enumerate such isomorphism classes by computing the characteristic polynomial of the discriminantal arrangement. With a certain restriction, the enumerated value is shown to be independent of the discriminantal arrangement. Later we observe that the restriction we impose on the type of hyperplane arrangements is a mild one and that this conditional restriction is quite generic. Moreover the restriction is defined in terms of a normal system being concurrency free which is a generic condition. We also discuss two examples of normal systems which are not concurrency free in the last section and enumerate the number of isomorphism classes.
