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A new lower bound for the density of planar Sets avoiding Unit Distances
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A new lower bound for the density of planar Sets avoiding Unit Distances
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Paper
A new lower bound for the density of planar Sets avoiding Unit Distances
2024
Overview
In a recently published article by G. Ambrus et al. a new upper bound for the density of an unit avoiding, periodic set is given as \\(0.2470\\), the first upper bound \\(< 1/4\\). A construction of Croft 1967 gave a lower bound \\(\\delta_C = 0.22936\\) for the density. To this date, no better construction with a higher lower bound has been given. In this article I give a construction planar sets with a higher density than Croft's tortoises. No explicit value for this density is given, it's just shown that Croft's density is a local minima of the density of a here constructed 1-parameter family of planar sets. So the densities are \\(> \\delta_C\\).
Publisher
Cornell University Library, arXiv.org
Subject
