Parallelograms and the VC-dimension of the distance sets
Combinatorics
2023-04-20 v1 Number Theory
Abstract
In this paper, we study the distribution of parallelograms and rhombi in a given set in the plane over arbitrary finite fields . As an application, we improve a recent result due to Fitzpatrick, Iosevich, McDonald, and Wyman (2021) on the Vapnik-Chervonenkis dimension of the induced distance graph. Our proofs are based on the discrete Fourier analysis.
Cite
@article{arxiv.2304.09375,
title = {Parallelograms and the VC-dimension of the distance sets},
author = {Thang Pham},
journal= {arXiv preprint arXiv:2304.09375},
year = {2023}
}
Comments
9 pages