A Lower Bound on the Density of Sphere Packings via Graph Theory

dc.creatorKrivelevich, Michael
dc.creatorLitsyn, Simon
dc.creatorVardy, Alexander
dc.date2004-02-09
dc.date.accessioned2026-07-07T05:05:16Z
dc.date.available2026-07-07T05:05:16Z
dc.descriptionUsing graph-theoretic methods we give a new proof that for all sufficiently large $n$, there exist sphere packings in $\R^n$ of density at least $cn2^{-n}$, exceeding the classical Minkowski bound by a factor linear in $n$. This matches up to a constant the best known lower bounds on the density of sphere packings due to Rogers, Davenport-Rogers, and Ball. The suggested method makes it possible to describe the points of such a packing with complexity $\exp(n\log n)$, which is significantly lower than in the other approaches.
dc.description6 pages, 2 postscript figures
dc.identifierhttps://arxiv.org/abs/math/0402132
dc.identifierhttp://arxiv.org/abs/math/0402132
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70103
dc.subjectCombinatorics
dc.subjectMetric Geometry
dc.subject05C90, 52C17 (Primary) 05C69, 11H31 (Secondary)
dc.titleA Lower Bound on the Density of Sphere Packings via Graph Theory
dc.typetext

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