具有大平均直径的超平面安排

Bisecting measures with hyperplane arrangements

We show that when $n$ is a power of two, any $nD$ measures in $\mathbb{R}^n$ can be bisected by an arrangement of $D$ hyperplanes.

Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids

A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter arrangements and the weak order through the poset of regions. For simplicial arrangements, posets of regions are in fact lattices. We update Grünbaum's catalogue, providing normals and invariants for all known sporadic simplicial arrangements with up to 37 lines. The weak order is known to be congruence normal, and congruence normality for simplicial arrangements can be determined using polyhedral cones called shards. In this article, we provide addition…

负曲流形中的超平面排列与相对双曲性

Hyperplane arrangements in negatively curved manifolds and relative hyperbolicity

我们证明了由负曲率流形中的超平面安排所产生的某些非球面流形具有相对双曲的基本群。

Birational Geometry of Matroids and Abstract Hyperplane Arrangements

A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering hyperplane arrangements, which give rise to convex polytopes called matroid polytopes. Much research has been conducted on these three areas: matroids, matroid polytopes, and hyperplane arrangements. However, substantial gaps in our knowledge remain, and the correspondence diagram between those areas needs to be more extensive. For instance, currently, there is…