English

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.

Keywords

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

R2 v1 2026-06-22T08:58:08.836Z