On the Geometry and Computational Complexity of Radon Partitions in the Integer Lattice

  title={On the Geometry and Computational Complexity of Radon Partitions in the Integer Lattice},
  author={Shmuel Onn},
  journal={SIAM J. Discrete Math.},
The following integer analogue of a Radon partition in aane space R d is studied: A partition (S; T) of a set of integer points in R d is an integral Radon partition if the convex hulls of S and T have an integer point in common. The Radon number r(d) of an appropriate convexity space on the integer lattice Z d is then the innmum over those natural numbers n such that any set of n points or more in Z d has an integral Radon partition. An (2 d) lower bound and an O(d2 d) upper bound on r(d) are… CONTINUE READING

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