论文标题
通用矫形器
Generic Orthotopes
论文作者
论文摘要
本文研究了大型的一般类正交多型，我们可以称为“通用正位”。这些物体源于向传统拓扑，结构或组合考虑因素特别好的正交多层代表Coxeter复合物的愿望。通用的矫形器具有宜人的“同质性”特性，有点像欧几里得空间的平滑界限紧凑子集。因此，一旦我们要求正交多层的每个顶点都是花卉排列，如这里所定义的，花卉布置也描述了许多衍生结构，例如面部和横截面。我们还使用几个自然定义的花卉排列定义的统计数据给出了通用正直的体积和欧拉特征的公式。
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect to traditional topological, structural, or combinatorial considerations. Generic orthotopes have a pleasant "homogeneity" property, somewhat like a smoothly bounded compact subset of Euclidean space. Thus, as soon as we demand that every vertex of an orthogonal polytope be a floral arrangement, as defined here, many derivative structures such as faces and cross-sections are also described by floral arrangements. We also give formulas for the volume and Euler characteristic of a generic orthotope using a couple of statistics that are defined naturally for floral arrangements.
