Helly numbers for quantitative Helly-type results
Abstract
We obtain three Helly-type results. First, we establish a Quantitative Colorful Helly-type theorem with the optimal Helly number 2 d 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 2 d + 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) 3 d + 1 ; however, we have no reason to believe that this bound is sharp.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Journal of Combinatorial Theory Series A
- Volume
- 220
- Pages
- 106160–106160
- Publication date
- 16 January 2026
- Language
- EN