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Density Estimates of 1-Avoiding Sets via Higher Order Correlations
Discrete & Computational Geometry ( IF 0.8 ) Pub Date : 2020-12-10 , DOI: 10.1007/s00454-020-00263-3
Gergely Ambrus , Máté Matolcsi

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.

中文翻译:

通过高阶相关性估计 1-Avoiding 集的密度

我们将单位距离处不包含两个点的平面可测集 A 的密度的最著名上限提高到 0.25442。我们结合使用傅里叶分析和线性规划方法来获得结果。该估计是通过利用 A 中的三阶相关性获得对 A 的自相关函数的新线性约束来实现的,这是以前没有研究过的概念。
更新日期:2020-12-10
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