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Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets
- Author(s): De Loera, JA
- La Haye, RN
- Rolnick, D
- Soberón, P
- et al.
Published Web Location
https://doi.org/10.1007/s00454-016-9858-3Abstract
© 2017, Springer Science+Business Media New York. This paper presents a new variation of Tverberg’s theorem. Given a discrete set S of Rd, 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 Carathéodory’s theorems.