由距离和点积确定的点构形的界
Bounds on point configurations determined by distances and dot products
摘要：
本文研究了Erd \H os的单位距离问题的一个变形族，它涉及从一个大的有限点集中选取的点对之间的距离和点积.具体来说，给定一个大有限集$n$点集$E$，我们寻找有多少个$k$点子集满足一组基于距离或点积的点对之间的关系的界限。我们调查了一些最近的工作在该地区，并提出了几个新的，更一般的家庭的界限。
英文摘要：
We study a family of variants of Erd\H os' unit distance problem, concerning distances and dot products between pairs of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, we look for bounds on how many subsets of $k$ points satisfy a set of relationships between point pairs based on distances or dot products. We survey some of the recent work in the area and present several new, more general families of bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
