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arXiv · 1603.05525

Quantitative Tverberg theorems over lattices and other discrete sets

J. A. De Loera·R. N. La Haye·D. Rolnick·P. Soberón
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Abstract

This paper presents a new variation of Tverberg's theorem. Given a discrete set $S$ of $R^d$, we study the number of points of $S$ needed to guarantee the existence of an $m$-partition of the points such that the intersection of the $m$ convex hulls of the parts contains at least $k$ points of $S$. The proofs of the main results require new quantitative versions of Helly's and Carathéodory's theorems.

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J. A. De Loera, R. N. La Haye, D. Rolnick, P. Soberón. 2016-03-18. Quantitative Tverberg theorems over lattices and other discrete sets. https://arxiv.org/abs/1603.05525

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