Minkowski Arrangements of Spheres |
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Authors: | Károly Böröczky László Szabó |
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Affiliation: | (1) Eötvös Loránd University, Budapest, Hungary, HU;(2) Computer and Automation Research Institute, Budapest, Hungary, HU |
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Abstract: | Let be a non-negative number not greater than 1. Consider an arrangement of (not necessarily congruent) spheres with positive homogenity in the n-dimensional Euclidean space, i.e., in which the infimum of the radii of the spheres divided by the supremum of the radii of the spheres is a positive number. With each sphere S of associate a concentric sphere of radius times the radius of S. We call this sphere the -kernel of S. The arrangement is said to be a Minkowski arrangement of order if no sphere of overlaps the -kernel of another sphere. The problem is to find the greatest possible density of n-dimensional Minkowski sphere arrangements of order . In this paper we give upper bounds on for . |
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Keywords: | 2000 Mathematics Subject Classification: 52C17 |
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