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arXiv · 2110.02415

Exponentially sized pointsets with angles less than 61 degrees

Miroslav Marinov
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Abstract

We prove that any set of points in $\mathbb{R}^d$, any three of which form an angle less than $\fracπ{3} + c$, has size $(1+Θ(c))^d$ for sufficiently small $c>0$. The proof is based on a refinement of an approach by Erdős and Füredi. The lower bound is relying on a problem about large hypegraphs with small edge intersections, while the upper bound is tightly connected to the problem of packing disjoint caps on a sphere.

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Miroslav Marinov. 2022-07-15. Exponentially sized pointsets with angles less than 61 degrees. https://arxiv.org/abs/2110.02415

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