论文标题
面部计数拓扑超平面布置
Face Counting for Topological Hyperplane Arrangements
论文作者
论文摘要
切割蛋糕后确定碎片数量是一个经典问题。罗伯茨（Roberts，1887）通过计算按线切割的平面中包含的腔室数来提供了精确的解决方案。大约88年后，Zaslavsky（1975）甚至计算了超平面布置的F-顺式式，因此推断了后者的腔室数量。最近，Forge＆Zaslavsky（2009）引入了拓扑超平面布置的更通用的结构。本文计算了这种布置跨性别时的F-多项式，因此可以推断出它们的腔室数量。
Determining the number of pieces after cutting a cake is a classical problem. Roberts (1887) provided an exact solution by computing the number of chambers contained in a plane cut by lines. About 88 years later, Zaslavsky (1975) even computed the f-polynomial of a hyperplane arrangement, and consequently deduced the number of chambers of that latter. Recently, Forge & Zaslavsky (2009) introduced the more general structure of topological hyperplane arrangements. This article computes the f-polynomial of such arrangements when they are transsective, and therefore deduces their number of chambers.
