Density Estimates of 1-Avoiding Sets via Higher Order Correlations-Reference-Cited by-同舟云学术

Density Estimates of 1-Avoiding Sets via Higher Order Correlations

Published:2020-12-10 Issue: Volume: Page:
ISSN:0179-5376
Container-title:Discrete & Computational Geometry
language:en
Short-container-title:Discrete Comput Geom

Author:

Ambrus Gergely^ORCID,Matolcsi Máté

Abstract

AbstractWe 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.

Funder

Nemzeti Kutatási Fejlesztési és Innovációs Hivatal

Magyar Tudományos Akadémia

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science

Link

http://link.springer.com/content/pdf/10.1007/s00454-020-00263-3.pdf

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