Geodesic
A Voronoi Poset
Journal for geometry and graphics, Tome 7 (2003) no. 1, pp. 041-052 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 recall symmetry relations for the number of cells, number of vertices and number of circles of certain orders. We introduce a poset Π(S) that consists of the k-th order Voronoi cells for all k = 1,...,n, that occur for some set S. We prove that there exists a rank function on Π(S) and moreover that the number of elements of odd rank equals the number of elements of even rank of Π(S), provided that n is odd.
Classification : 52B55, 68U05
Mots-clés : k-th order Voronoi diagrams, k-sets, posets, point configurations 
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     author = {R. C. Lindenbergh},
     title = {A {Voronoi} {Poset}},
     journal = {Journal for geometry and graphics},
     pages = {041--052},
     year = {2003},
     volume = {7},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a2/}
}
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R. C. Lindenbergh. A Voronoi Poset. Journal for geometry and graphics, Tome 7 (2003) no. 1, pp. 041-052. http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a2/