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ELTE lágymányosi campus, déli épület (1117 Budapest, Pázmány Péter s.1/C), 3-716 terem
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Description

We study the growth of r_k, the k-th Radon number, in convexity spaces. If r_2 is finite, we present an improved upper bound on r_k. We also investigate Eckhoff's conjecture on the growth of r_k, which has been proven to be true when r_2 = 3. However, when r_2 = 4, we construct a family of convexity spaces where Echkoff's conjecture fails. 

 

bibliography:

B. Bukh: Radon partitions in convexity spaces, arXiv.