I: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences II: Department of Mathematics, University College London I: H-1364 Budapest, P.O.B. 127, Hungary II: Gower Street, London Wc1e 6bt, England
Institute for Theoretical Computer Science and Department of Applied Mathematics, Charles University Malostranské Nám. 25, 118 00 Praha 1, Czech Republic
A subset A of a finite set P of points in the plane is called an empty polygon, if each point of A is a vertex of the convex hull of A and the convex hull of A contains no other points of P. We construct a set of n points in general position in the plane with only ˜1.62n2 empty triangles, ˜1.94n2 empty quadrilaterals, ˜1.02n2 empty pentagons, and ˜0.2n2 empty hexagons.
Bárány, I. and Füredi, Z., Empty simplices in Euclidean space, Canadian Math. Bull.30 (1987), 436-445. MR89g:52004
'Empty simplices in Euclidean space' () 30Canadian Math. Bull.: 436-445.
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Balog, A. and Deshouillers, J-M., On some convex lattice polytopes, in: Number theory in progress, Volume 2: Elementary and analytic number theory (K. Györy et al., eds.), de Gruyter, Berlin 1999, 591-606. MR2000f:11083
Number theory in progress, Volume 2: Elementary and analytic number theory, () 591-606.
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