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arXiv · 2501.03645

Big convex polytopes or rich hyperplanes

Koki Furukawa
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Abstract

For natural numbers $n$ and $l > d \geq 2$, let $ES_d(l,n)$ be the minimum $N$ such that any set of at least $N$ points in $\mathbb{R}^d$ contains either $l$ points contained in a common $(d-1)$-dimensional hyperplane or $n$ points in convex position. In this paper, we give the upper and lower bounds for $ES_d(l,n)$.

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Koki Furukawa. 2025-05-30. Big convex polytopes or rich hyperplanes. https://arxiv.org/abs/2501.03645

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