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 Locationhttps://doi.org/10.1007/s00454-016-9858-3
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.