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Lattices and packings in higher dimensions
2010A lattice in \(\mathbb{R}^3\) is a Λ that can be written as the set of integer combinations of three linearly independent vectors \(\{a,b,c\}\), say \(\Lambda= \mathbb{Z} \cdot a+\mathbb{Z} \cdot b+\mathbb{Z} \cdot c\). As in Sect. IX.4, two Euclidean invariants are immediately associated with a lattice; they are practically dictated when we seek to ...
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1988
We propose and motivate a new variant of the wellknown two-dimensional binpacking problem (orthogonal and oriented rectangle packing). In our model, we are allowed to cut a rectangle and move the parts horizontally. We describe two relatively simple algorithms for this problem and determine their asymptotic performance ratios.
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We propose and motivate a new variant of the wellknown two-dimensional binpacking problem (orthogonal and oriented rectangle packing). In our model, we are allowed to cut a rectangle and move the parts horizontally. We describe two relatively simple algorithms for this problem and determine their asymptotic performance ratios.
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Self-similarity and packing dimension
2016Christopher J. Bishop, Yuval Peres
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On the Closest Packing of Spheres in n Dimensions
The Annals of Mathematics, 1947openaire +2 more sources