Quantitative combinatorial geometry for continuous parameters
Metric Geometry
2016-03-21 v2 Combinatorics
Abstract
We prove variations of Carath\'eodory's, Helly's and Tverberg's theorems where the sets involved are measured according to continuous functions such as the volume or diameter. Among our results, we present continuous quantitative versions of Lov\'asz's colorful Helly theorem, B\'ar\'any's colorful Carath\'eodory's theorem, and the colorful Tverberg theorem.
Cite
@article{arxiv.1603.05523,
title = {Quantitative combinatorial geometry for continuous parameters},
author = {J. A. De Loera and R. N. La Haye and D. Rolnick and P. Soberón},
journal= {arXiv preprint arXiv:1603.05523},
year = {2016}
}
Comments
22 pages. arXiv admin note: substantial text overlap with arXiv:1503.06116