• DOI:10.1016/J.AIM.2011.01.009
Corpus ID: 115161963

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}
}

• P. Blagojevic, B. Matschke, G. Ziegler
• Published 2009
• Mathematics
• arXiv: Algebraic Topology

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

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed