论文标题
尺寸为白鲸
Sizing the White Whale
论文作者
论文摘要
我们提出了一个计算，凸出船体的无自由框架，该框架利用了地位的组合结构，例如其对称组，以生成其顶点的所有规范代表。我们通过生成所有1 955 230 985 997 140 $ 9 $维白鲸的顶点来说明拟议的框架。我们还计算该界限的边缘数量达到尺寸$ 9 $，并展示了一个顶点的家庭，其学位在维度上是指数的。白鲸是所有$ 2^d-1 $ non-Zero $ 0/1 $ -D $ D $二维向量的Minkowski总和。由这些向量正常的超平面组成的白鲸的中央超平面布置被称为共振布置，并已在各种情况下进行了研究，包括代数几何形状，数学物理学，经济学，心理学和代表理论。
We propose a computational, convex hull free framework that takes advantage of the combinatorial structure of a zonotope, as for example its symmetry group, to orbitwise generate all canonical representatives of its vertices. We illustrate the proposed framework by generating all the 1 955 230 985 997 140 vertices of the $9$-dimensional White Whale. We also compute the number of edges of this zonotope up to dimension $9$ and exhibit a family of vertices whose degree is exponential in the dimension. The White Whale is the Minkowski sum of all the $2^d-1$ non-zero $0/1$-valued $d$-dimensional vectors. The central hyperplane arrangement dual to the White Whale, made up of the hyperplanes normal to these vectors, is called the resonance arrangement and has been studied in various contexts including algebraic geometry, mathematical physics, economics, psychometrics, and representation theory.
