论文标题
在$ {\ bf r}^d $中的套装的基础性上
On the cardinality of sets in ${\bf R}^d$ obeying a slightly obtuse angle bound
论文作者
论文摘要
在本文中，我们明确估计子集$ a \ subset \ r^{d} $中的点数作为最大角度$ \ angle a $的函数，这些点的任何三个点形式中的任何三个点，提供$ \ angle a <θ_d：= \ arccos（ - \ arccos（ - \ frac 1 {d}）\ in（\ frac 1 {d}）\ in（frac 1 {d}）\ in（frac 1 {d}）\ in（frac 1 {d}）\ in（frac 1 {d}）$。我们还显示$ \ Angle a <θ_d$确保$ a $与凸polytope的顶点集合。这项研究是由保罗·埃德斯（Paul Erds）的问题，并间接地是由拉斯兹洛·费耶斯·托斯（LászlóFejesTóth）的猜想。
In this paper we explicitly estimate the number of points in a subset $A \subset \R^{d}$ as a function of the maximum angle $\angle A$ that any three of these points form, provided $\angle A < θ_d := \arccos(-\frac 1 {d}) \in (π/2,π)$. We also show $\angle A < θ_d$ ensures that $A$ coincides with the vertex set of a convex polytope. This study is motivated by a question of Paul Erdős and indirectly by a conjecture of László Fejes Tóth.
