Claremont Reu Abstract of L. Fukshansky’s Group: on Well-rounded Sublattices of the Hexagonal Lattice
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چکیده
Kepler’s Conjecture, recently proved by T. Hales, states that the densest packing of spheres in 3-space has spheres centered along the face-centered cubic (fcc) lattice. A lattice is a free Z-module formed by taking the span of a collection of linearly independent vectors in R over the integers. The two-dimensional analogue of Kepler’s Conjecture, proved by L. F. Toth in 1940, states that the densest packing of circles in the plane is the hexagonal lattice (see [2], [7] for an overview of the area, and [3] for introductory lecture notes). We may define the hexagonal lattice as the set of all integral linear combinations of the vectors [ 1 0 ]
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تاریخ انتشار 2009