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- W2980760300 abstract "It is well known that the lattice packing density and the lattice covering density of a triangle are $frac{2}{3}$ and $frac{3}{2}$ respectively. We also know that the lattices that attain these densities both are unique. Let $delta_{L}(K)$ and $vartheta_{L}(K)$ denote the lattice packing density and the lattice covering density of $K$, respectively. In this paper, I study the lattice packings and coverings for a special class of convex disks, which includes all triangles and convex quadrilaterals. In particular, I determine the densities $delta_{L}(Q)$ and $vartheta_{L}(Q)$, where $Q$ is an arbitrary convex quadrilateral. Furthermore, I also obtain all of lattices that attain these densities. Finally, I show that $delta_{L}(Q)vartheta_{L}(Q)geq 1$ and $frac{1}{delta_{L}(Q)}+frac{1}{vartheta_{L}(Q)}geq 2$, for each convex quadrilateral $Q$." @default.
- W2980760300 created "2019-10-25" @default.
- W2980760300 creator A5006234306 @default.
- W2980760300 date "2014-11-18" @default.
- W2980760300 modified "2023-09-27" @default.
- W2980760300 title "On the Lattice Packings and Coverings of Convex Quadrilaterals" @default.
- W2980760300 hasPublicationYear "2014" @default.
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