Radon partitions in convexity spaces
Abstract
Tverberg's theorem asserts that every (k1)(d+1)+1 points in R^d can be partitioned into k parts, so that the convex hulls of the parts have a common intersection. Calder and Eckhoff asked whether there is a purely combinatorial deduction of Tverberg's theorem from the special case k=2. We dash the hopes of a purely combinatorial deduction, but show that the case k=2 does imply that every set of O(k^2 log^2 k) points admits a Tverberg partition into k parts.
 Publication:

arXiv eprints
 Pub Date:
 September 2010
 DOI:
 10.48550/arXiv.1009.2384
 arXiv:
 arXiv:1009.2384
 Bibcode:
 2010arXiv1009.2384B
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Computational Geometry;
 Mathematics  Metric Geometry;
 52A01 (Primary);
 05D05;
 06A15;
 52A37 (Secondary)
 EPrint:
 11 pages