منابع مشابه
Cube packings, second moment and holes
We consider tilings and packings of R by integral translates of cubes [0, 2[, which are 4Z-periodic. Such cube packings can be described by cliques of an associated graph, which allow us to classify them in dimension d ≤ 4. For higher dimension, we use random methods for generating some examples. Such a cube packing is called non-extendible if we cannot insert a cube in the complement of the pa...
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We describe an adaptation of the billiard algorithm for finding dense packings of equal spheres inside a domain of the euclidean space. In order to improve the convergence of this stochastic algorithm, we introduce systematic perturbations in it. We apply this perturbed billiard algorithm in the case of n spheres in a cube and display all the optimal and best known packings up to n = 32. We imp...
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We consider the problem of packing n disks of unit diameter in the plane so as to minimize the second moment about their centroid. Our main result is an algorithm which constructs packings that are optimal among hexagonal packings. Using the algorithm, we prove that, except for n = 212, the n-point packings obtained by Graham and Sloane [1] are optimal among hexagonal packings. We also prove a ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2006.01.008