Density estimates of 1-avoiding sets via higher order correlations
Metric Geometry
2020-12-15 v3
Abstract
We improve the best known upper bound on the density of a planar measurable set A containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The estimate is achieved by means of obtaining new linear constraints on the autocorrelation function of A utilizing triple-order correlations in A, a concept that has not been previously studied.
Cite
@article{arxiv.1809.05453,
title = {Density estimates of 1-avoiding sets via higher order correlations},
author = {Gergely Ambrus and Máté Matolcsi},
journal= {arXiv preprint arXiv:1809.05453},
year = {2020}
}
Comments
11 pages, 2 figures