Packing dimension information

the packing dimension is one of a number of concepts that can be used to define the dimension of a subset of a metric space. Packing dimension is in...

dimension that, like Hausdorff dimension, is defined using coverings by balls Intrinsic dimension Packing dimension Fractal dimension MacGregor Campbell, 2013...

of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres...

sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packing must be without overlaps between goods and other...

}(X):=\inf\{d\geq 0:C_{H}^{d}(X)=0\}.} Packing dimension Assouad dimension Local connected dimension Degree dimension: describes the fractal nature of the...

Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. If...

{some\ c.e.} \ s\mathrm {-gale\ succeeds\ on\ } X\}} . The effective packing dimension of X is inf { s : s o m e   c . e .   s − g a l e   s u c c e e d...

items in each bin. Other variants are two-dimensional bin packing, three-dimensional bin packing, bin packing with delivery, BPPLIB - a library of surveys...

continuous on the right for all t ≥ 0. Packing dimension is constructed in a very similar way to Hausdorff dimension, except that one "packs" E from inside...

Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It...

Publishing, 2016), p. 5. Boyd, David W. (1973), "The residual set dimension of the Apollonian packing", Mathematika, 20 (2): 170–174, doi:10.1112/S0025579300004745...

two-dimensional Euclidean plane, Joseph Louis Lagrange proved in 1773 that the highest-density lattice packing of circles is the hexagonal packing arrangement...

The strip packing problem is a 2-dimensional geometric minimization problem. Given a set of axis-aligned rectangles and a strip of bounded width and infinite...

fixed. Circle packing in a rectangle Square packing in a square De Bruijn's theorem: packing congruent rectangular bricks of any dimension into rectangular...

Apollonian sphere packing is the three-dimensional equivalent of the Apollonian gasket. The principle of construction is very similar: with any four spheres...

Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder...

Square packing is a packing problem where the objective is to determine how many congruent squares can be packed into some larger shape, often a square...

Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose...

simplify computation of the packing measure. An equivalent statement of the open set condition is to require that the s-dimensional Hausdorff measure of the...

Equilateral dimension Spherical code Soddy's hexlet Cylinder sphere packing Conway, John H.; Neil J.A. Sloane (1999). Sphere Packings, Lattices and...

In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum...

October 2016). "Three Variable Dimension Surfaces". ResearchGate. The Fractal dimension of the apollonian sphere packing Archived 6 May 2016 at the Wayback...

Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square...