On empty convex polytopes |
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| Authors: | Tibor Bisztriczky Heiko Harborth |
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| Affiliation: | (1) Department of Mathematics and Statistics, University of Calgary, 2500 University Dr. N. W., T2N 1N4 Calgary, Alberta, Canada;(2) Diskrete Mathematik, Technische Universität Braunschweig, Pockelsstr. 14, D-38106 Braunschweig, Germany |
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| Abstract: | Letn andd be integers,n>d  2. We examine the smallest integerg(n,d) such that any setS of at leastg(n,d) points, in general position in Ed, containsn points which are the vertices of an empty convexd-polytopeP, that is, S intP = 0. In particular we show thatg(d+k, d) = d+2k–1 for 1  k iLd/2rL+1. |
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