.png){kind=icon}
.png){kind=icon}
Return
Helly numbers for quantitative Helly-type results
.png){kind=icon}
OA
AI
DOI：10.1016/j.jcta.2026.106160.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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. (c) 2026 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
Keywords:
Colorful Helly-type theorem
Log-concave function
John ellipsoid
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
J
IF:
1.2
Papers:
42
Citations:
0