A Voronoi Poset
نویسنده
چکیده
Given a set S of n points in general position, we consider all k-th order Voronoi diagrams on S, for k = 1, . . . , n, simultaneously. We deduce symmetry relations for the number of faces, number of vertices and number of circles of certain orders. These symmetry relations are independent of the position of the sites in S. As a consequence we show that the reduced Euler characteristic of the poset of faces equals zero whenever n odd. 1 Notation. A(S) – the arrangement defined by all bisectors in S. B(a, b) – the bisector of a and b. CH(S) – the convex hull of S. δU – the boundary of the set U . Vk(S) – k-th order Voronoi diagram on S
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