Bounds on Point Configurations Determined by Distances and Dot Products
We study a family of variants of Erdő’s 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.
Gunter S., Palsson E., Rhodes B., Senger S. (2021) Bounds on Point Configurations Determined by Distances and Dot Products. In: Nathanson M.B. (eds) Combinatorial and Additive Number Theory IV. CANT 2020. Springer Proceedings in Mathematics & Statistics, vol 347. Springer, Cham. https://doi.org/10.1007/978-3-030-67996-5_12
Springer Proceedings in Mathematics and Statistics