论文标题
点产品链
Dot product chains
论文作者
论文摘要
我们研究了ERD \ H OS'单位距离问题的变体，涉及从大量有限点集选择的连续对点之间的点产物。具体而言，给定一组有限的$ n $点$ e $，以及一系列非零点产品$（α_1，\ ldots，α_k）$，我们在最大可能的分组$（a_1，\ dots）的最大数量（a_1，\ dots）上给出上限和下限A_ {J+1} =α_J$每$ 1 \ leq J \ leq k $。
We study a variant of Erd\H os' unit distance problem, concerning dot products between successive pairs of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, and a sequence of nonzero dot products $(α_1,\ldots,α_k)$, we give upper and lower bounds on the maximum possible number of tuples of distinct points $(A_1,\dots, A_{k+1})\in E^{k+1}$ satisfying $A_j \cdot A_{j+1}=α_j$ for every $1\leq j \leq k$.
