Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets

Authors :: Reuben N. Haye
David Rolnick
Jesús A. De Loera
Pablo Soberón
Source :: Discrete & Computational Geometry, vol 58, iss 2, De Loera, JA; La Haye, RN; Rolnick, D; & Soberón, P. (2017). Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets. Discrete and Computational Geometry, 58(2), 435-448. doi: 10.1007/s00454-016-9858-3. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/2037z49w, Discrete and Computational Geometry, vol 58, iss 2
Publication Year :: 2017
Publisher :: eScholarship, University of California, 2017.
Abstract: This paper presents a new variation of Tverberg's theorem. Given a discrete set $S$ of $R^d$, we study the number of points of $S$ needed to guarantee the existence of an $m$-partition of the points such that the intersection of the $m$ convex hulls of the parts contains at least $k$ points of $S$. The proofs of the main results require new quantitative versions of Helly's and Carath\'eodory's theorems.<br />Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1503.06116

Database :: OpenAIRE
Journal :: Discrete & Computational Geometry, vol 58, iss 2, De Loera, JA; La Haye, RN; Rolnick, D; & Soberón, P. (2017). Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets. Discrete and Computational Geometry, 58(2), 435-448. doi: 10.1007/s00454-016-9858-3. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/2037z49w, Discrete and Computational Geometry, vol 58, iss 2
Accession number :: edsair.doi.dedup.....78308f493439cd86e409079350cfe605

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