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arXiv · 2409.15048

Helly numbers for Quantitative Helly-type results

G. Ivanov·M. Naszodi
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Abstract

We obtain three Helly-type results. First, we establish a Quantitative Colorful Helly-type theorem with the optimal Helly number \(2d\) concerning the diameter of the intersection of a family of convex bodies. Second, we prove a Quantitative Helly-type theorem with the optimal Helly number \(2d+1\) for the pointwise minimum of logarithmically concave functions. Finally, we present a colorful version of the latter result with Helly number (number of color classes) \(3d+1\); however, we have no reason to believe that this bound is sharp.

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G. Ivanov, M. Naszodi. 2024-09-23. Helly numbers for Quantitative Helly-type results. https://arxiv.org/abs/2409.15048

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