Packing and Covering with Centrally Symmetric Convex Disks |
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| Authors: | Dan Ismailescu Brian Kim |
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| Institution: | 1. Department of Mathematics, 103 Hofstra University, Hempstead, New York, NY, 11549, USA
2. Fu Foundation School of Engineering and Applied Sciences, Columbia University, 2920 Broadway, New York, NY, 10027, USA
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| Abstract: | Given a convex disk K (a convex compact planar set with nonempty interior), let δ L (K) and θ L (K) denote the lattice packing density and the lattice covering density of K, respectively. We prove that for every centrally-symmetric convex disk K we have that $$ 1\le\delta_L(K)\theta_L(K)\le1.17225\ldots $$ The left inequality is tight and it improves a 10-year old result. |
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