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arXiv · 1809.05453

Density estimates of 1-avoiding sets via higher order correlations

Gergely Ambrus·Máté Matolcsi
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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.

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Gergely Ambrus, Máté Matolcsi. 2020-10-20. Density estimates of 1-avoiding sets via higher order correlations. https://doi.org/10.1007/s00454-020-00263-3

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