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arXiv · 1810.02671

On the number of vertices of projective polytopes

Natalia García-Colín·Luis Pedro Montejano·Jorge Luis Ramírez Alfonsín
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Abstract

Let $X$ be a configuration of $n$ points in $\mathbb{R}^d$. What is the maximum number of vertices that $conv(T(X))$ can have among all the possible permissible projective transformations $T$? In this paper, we investigate this and connected questions. After presenting several upper bounds, we study a closely related problem (via Gale transforms) concerning the number of minimal Radon partitions of a set of points. We then present some bounds for this number that enable us to partially answer a question due to Pach and Szegedy. We also discuss another related problem concerning the size of topes in arrangements of hyperplanes.

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Natalia García-Colín, Luis Pedro Montejano, Jorge Luis Ramírez Alfonsín. 2018-10-05. On the number of vertices of projective polytopes. https://arxiv.org/abs/1810.02671

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