A Lower Bound on the Density of Sphere Packings via Graph Theory
| dc.creator | Krivelevich, Michael | |
| dc.creator | Litsyn, Simon | |
| dc.creator | Vardy, Alexander | |
| dc.date | 2004-02-09 | |
| dc.date.accessioned | 2026-07-07T05:05:16Z | |
| dc.date.available | 2026-07-07T05:05:16Z | |
| dc.description | Using 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.description | 6 pages, 2 postscript figures | |
| dc.identifier | https://arxiv.org/abs/math/0402132 | |
| dc.identifier | http://arxiv.org/abs/math/0402132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70103 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 05C90, 52C17 (Primary) 05C69, 11H31 (Secondary) | |
| dc.title | A Lower Bound on the Density of Sphere Packings via Graph Theory | |
| dc.type | text |