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- Author or Editor: Imre Bárány x
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Abstract
We show by a construction that there are at least exp {cV (d−1)/(d+1)} convex lattice polytopes in ℝd of volume V that are different in the sense that none of them can be carried to an other one by a lattice preserving affine transformation.
Summary
Let
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 ˜1.62n 2 empty triangles, ˜1.94n 2 empty quadrilaterals, ˜1.02n 2 empty pentagons, and ˜0.2n 2 empty hexagons.