A geometric proof of the colored Tverberg theorem
Matoušek, Jiří
Martin Tancer
Uli Wagner
The colored Tverberg theorem asserts that for eve;ry d and r there exists t=t(d,r) such that for every set C ⊂ ℝ d of cardinality (d + 1)t, partitioned into t-point subsets C 1, C 2,...,C d+1 (which we think of as color classes; e. g., the points of C 1 are red, the points of C 2 blue, etc.), there exist r disjoint sets R 1, R 2,...,R r⊆C that are rainbow, meaning that {pipe}R i∩C j{pipe}≤1 for every i,j, and whose convex hulls all have a common point. All known proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojević, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof more concrete and intuitive, and accessible to a wider audience.
Springer
2012
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/2438
Matoušek J, Tancer M, Wagner U. A geometric proof of the colored Tverberg theorem. <i>Discrete & Computational Geometry</i>. 2012;47(2):245-265. doi:<a href="https://doi.org/10.1007/s00454-011-9368-2">10.1007/s00454-011-9368-2</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00454-011-9368-2
info:eu-repo/semantics/closedAccess