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• W2171453190 abstract "In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in $mathbb{R}^n$; this theorem is a generalization of the linear programming bound for sphere packings. We illustrate its use by computing an upper bound for the maximum density of packings of regular pentagons in the plane. Our computational approach is numerical and uses a combination of semidefinite programming, sums of squares, and the harmonic analysis of the Euclidean motion group. We show how, with some extra work, the bounds so obtained can be made rigorous." @default.
• W2171453190 created "2016-06-24" @default.
• W2171453190 creator A5046618878 @default.
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• W2171453190 date "2018-01-01" @default.
• W2171453190 modified "2023-09-27" @default.
• W2171453190 title "Computing Upper Bounds for the Packing Density of Congruent Copies of a Convex Body" @default.
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• W2171453190 doi "https://doi.org/10.1007/978-3-662-57413-3_7" @default.
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