A Geometric Proof of the Colored Tverberg Theorem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10125606" target="_blank" >RIV/00216208:11320/12:10125606 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00454-011-9368-2" target="_blank" >http://dx.doi.org/10.1007/s00454-011-9368-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-011-9368-2" target="_blank" >10.1007/s00454-011-9368-2</a>

Result language
angličtina
Original language name
A Geometric Proof of the Colored Tverberg Theorem
Original language description
The colored Tverberg theorem asserts that for every d and r there exists t=t(d,r) such that for every set C in 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_1are red, the points of C_2 blue, etc.), there exist r disjoint sets R_1, R_2, ... ,R_r subset of C that are rainbow, meaning that the size of the intersection of R_i and C_j is at most 1 for every i, j, and whose convex hulls all have a common point. Allknown proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojevic, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof moreconcrete and intuitive, and accessible to a wider audience.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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