A Voronoi poset
Metric Geometry
2007-05-23 v1 Combinatorics
Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/9905018,
title = {A Voronoi poset},
author = {Roderik C. Lindenbergh},
journal= {arXiv preprint arXiv:math/9905018},
year = {2007}
}
Comments
14 pages 4 figures