Affiliation:
1. University of Maine Orono Maine USA
2. Johannes Kepler Universität Linz Austria
3. Missouri State University Springfield Missouri USA
Abstract
AbstractLet be a point set with cardinality . We give an improved bound for the number of dot products determined by , proving that
A crucial ingredient in the proof of this bound is a new superquadratic expander involving products and shifts. We prove that, for any finite set , there exist such that
This is derived from a more general result concerning growth of sets defined via convexity and sum sets, and which can be used to prove several other expanders with better than quadratic growth. The proof develops arguments from Hanson, Roche‐Newton, and Rudnev [Combinatorica, to appear], and uses predominantly elementary methods.
Funder
Austrian Science Fund
National Science Foundation
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. A better than exponent for iterated sums and products over;Mathematical Proceedings of the Cambridge Philosophical Society;2024-05-10
2. Convexity, Elementary Methods, and Distances;Discrete & Computational Geometry;2024-02-03
3. Convexity, Squeezing, and the Elekes-Szabó Theorem;The Electronic Journal of Combinatorics;2024-01-12