Quantitative Tverberg, Helly, & Carath\'eodory theorems
Metric Geometry
2015-04-03 v3 Combinatorics
Abstract
This paper presents sixteen quantitative versions of the classic Tverberg, Helly, & Caratheodory theorems in combinatorial convexity. Our results include measurable or enumerable information in the hypothesis and the conclusion. Typical measurements include the volume, the diameter, or the number of points in a lattice.
Cite
@article{arxiv.1503.06116,
title = {Quantitative Tverberg, Helly, & Carath\'eodory theorems},
author = {J. A. De Loera and R. N. La Haye and D. Rolnick and P. Soberón},
journal= {arXiv preprint arXiv:1503.06116},
year = {2015}
}
Comments
33 pages