Density Estimates of 1-Avoiding Sets via Higher Order Correlations

Density Estimates of 1-Avoiding Sets via Higher Order Correlations

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...

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Veröffentlicht in:Discrete & computational geometry 2022-06, Vol.67 (4), p.1245-1256
Hauptverfasser: Ambrus, Gergely, Matolcsi, Máté
Format: Artikel
Sprache:eng
Schlagworte:
Autocorrelation functions
Combinatorics
Computational Mathematics and Numerical Analysis
Density
Linear programming
Mathematics
Mathematics and Statistics
Upper bounds
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Zusammenfassung: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.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-020-00263-3