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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.
Abstract

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.

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