Ambrus, Gergely and Matolcsi, Máté (2020) Density Estimates of 1-Avoiding Sets via Higher Order Correlations. DISCRETE AND COMPUTATIONAL GEOMETRY. pp. 1-12. ISSN 0179-5376 (print); 1432-0444 (online)
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Official URL: https://doi.org/10.1007/s00454-020-00263-3
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. © 2020, The Author(s).
| Item Type: | Article |
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| Uncontrolled Keywords: | Chromatic number of the plane; Distance-avoiding sets; Linear programming; Harmonic analysis |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 01 Feb 2021 13:02 |
| Last Modified: | 01 Feb 2021 13:02 |
| URI: | http://real.mtak.hu/id/eprint/120383 |
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