Optimal bounds for a colorful Tverberg--Vrecica type problem

@article{Blagojevic2009OptimalBF,
  title={Optimal bounds for a colorful Tverberg--Vrecica type problem},
  author={P. Blagojevic and B. Matschke and G. Ziegler},
  journal={arXiv: Algebraic Topology},
  year={2009}
}
We prove the following optimal colorful Tverberg-Vrecica type transversal theorem: For prime r and for any k+1 colored collections of points C^l of size |C^l|=(r-1)(d-k+1)+1 in R^d, where each C^l is a union of subsets (color classes) C_i^l of size smaller than r, l=0,...,k, there are partition of the collections C^l into colorful sets F_1^l,...,F_r^l such that there is a k-plane that meets all the convex hulls conv(F_j^l), under the assumption that r(d-k) is even or k=0. Along the proof we… Expand
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