论文标题
在Minkowski空间中的$ K $ -Diametral点配置
On $k$-diametral point configurations in Minkowski spaces
论文作者
论文摘要
Minkowski $ d $ -space中$ K $ -Diametral点配置的结构与$ \ Mathbb {r}^d $中的$ k $ -antipodal点配置的属性密切相关。特别是，对于给定的$ k $ -diametral点配置，对于给定的$ k \ geq 2 $和$ d \ geq 2 $在Minkowski space中的平衡集中获得了$ k \ geq 2 $和$ d \ geq 2 $和$ d \ geq 2 $概括petty的结果（Proc。Am。Math。Math。29：369-374，1971）。此外，在欧几里得$ d $ -space中的$ k $ diametral点配置的最大尺寸得出的界限。在证明中，凸态方法与直径图的体积估计值和组合特性相结合。
The structure of $k$-diametral point configurations in Minkowski $d$-space is shown to be closely related to the properties of $k$-antipodal point configurations in $\mathbb{R}^d$. In particular, the maximum size of $k$-diametral point configurations of Minkowski $d$-spaces is obtained for given $k\geq 2$ and $d\geq 2$ generalizing Petty's results (Proc. Am. Math. Soc. 29: 369-374, 1971) on equilateral sets in Minkowski spaces. Furthermore, bounds are derived for the maximum size of $k$-diametral point configurations in Euclidean $d$-space. In the proofs convexity methods are combined with volumetric estimates and combinatorial properties of diameter graphs.
