2011/05/10 by Stephanie Vance · 53 citations
Chemistry · Materials Science · Mathematics · #Asymptotic formula #Atomic packing factor #Chemistry #Circle packing #Combinatorics #Constant (computer programming) #Crystallography #Geometry #Lattice (music) #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Natural density #Physics #Point processes and geometric inequalities #Quasicrystal Structures and Properties #Sphere packing #Upper and lower bounds #math.MG
paper · pdf · doi:10.1016/j.aim.2011.04.016
published in Advances in Mathematics 227(5), 2144-2156 (Elsevier BV) · 12 pages
openalex publication_date 2011/05/10 · arxiv created 2011/05/19 · arxiv updated 2011/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we prove an asymptotic lower bound for the sphere packing density in dimensions divisible by four. This asymptotic lower bound improves on previous asymptotic bounds by a constant factor and improves not just lower bounds for the sphere packing density, but also for the lattice sphere packing density and, in fact, the Hurwitz lattice sphere packing density.