On empty convex polytopes
- Cite this article as:
- Bisztriczky, T. & Harborth, H. J Geom (1995) 52: 25. doi:10.1007/BF01406823
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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.