Upper bounds for packings of spheres of several radii
Forum of Mathematics, Sigma, Tome 2 (2014)
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We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds for packings of spherical caps and of convex bodies through the use of semidefinite programming. We perform explicit computations, obtaining new bounds for packings of spherical caps of two different sizes and for binary sphere packings. We also slightly improve the bounds for the classical problem of packing identical spheres.
@article{10_1017_fms_2014_24,
author = {DAVID DE LAAT and FERNANDO M\'ARIO DE OLIVEIRA FILHO and FRANK VALLENTIN},
title = {Upper bounds for packings of spheres of several radii},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {2},
year = {2014},
doi = {10.1017/fms.2014.24},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2014.24/}
}
TY - JOUR AU - DAVID DE LAAT AU - FERNANDO MÁRIO DE OLIVEIRA FILHO AU - FRANK VALLENTIN TI - Upper bounds for packings of spheres of several radii JO - Forum of Mathematics, Sigma PY - 2014 VL - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2014.24/ DO - 10.1017/fms.2014.24 LA - en ID - 10_1017_fms_2014_24 ER -
%0 Journal Article %A DAVID DE LAAT %A FERNANDO MÁRIO DE OLIVEIRA FILHO %A FRANK VALLENTIN %T Upper bounds for packings of spheres of several radii %J Forum of Mathematics, Sigma %D 2014 %V 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2014.24/ %R 10.1017/fms.2014.24 %G en %F 10_1017_fms_2014_24
DAVID DE LAAT; FERNANDO MÁRIO DE OLIVEIRA FILHO; FRANK VALLENTIN. Upper bounds for packings of spheres of several radii. Forum of Mathematics, Sigma, Tome 2 (2014). doi: 10.1017/fms.2014.24
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