منابع مشابه
Segments in Ball Packings
Denote by B the n-dimensional unit ball centred at o. It is known that in every lattice packing of B there is a cylindrical hole of infinite length whenever n ≥ 3. As a counterpart, this note mainly proves the following result: For any fixed , > 0, there exist a periodic point set P (n, ) and a constant c(n, ) such that B + P (n, ) is a packing in R, and the length of the longest segment contai...
متن کاملPeriodic planar disc packings.
Several conditions are given when a packing of equal discs in a torus is locally maximally dense, where the torus is defined as the quotient of the plane by a two-dimensional lattice. Conjectures are presented that claim that the density of any collectively jammed packing, whose graph does not consist of all triangles, and the torus lattice is the standard triangular lattice, is at most (n/(n +...
متن کاملPeriodic Planar Disk Packings
Several conditions are given when a packing of equal disks in a torus is locally maximally dense, where the torus is defined as the quotient of the plane by a two-dimensional lattice. Conjectures are presented that claim that the density of any strictly jammed packings, whose graph does not consist of all triangles and the torus lattice is the standard triangular lattice, is at most n n+1 π √ 1...
متن کاملMaximal ball packings of symplectic-toric manifolds
Let (M, σ, ψ) be a symplectic-toric manifold of dimension at least four. This paper investigates the symplectic ball packing problem in the toral equivariant setting. We show that the set of toric symplectic ball packings of M admits the structure of a convex polytope. Previous work of the first author shows that up to equivalence, only (CP)2 and CP admit density one packings when n = 2 and onl...
متن کاملOn Free Planes in Lattice Ball Packings
This note, by studying relations between the length of the shortest lattice vectors and the covering minima of a lattice, mainly proves that for every d-dimensional packing lattice of balls one can find a 4-dimensional plane, parallel to a lattice plane, such that the plane meets none of the balls of the packing, provided the dimension d is large enough. On the other hand, we show that for cert...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2014
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-014-9636-z