The density of lattice sphere packings / A densidade de empacotamentos esfericos em reticulados
AUTOR(ES)
Ligia Rodrigues Bernabe Naves
DATA DE PUBLICAÇÃO
2009
RESUMO
This dissertation addresses the lattice theory with focus on packing density, which has many applications and allows to establish interesting connections between topics of linear algebra, calculus of several variables and discrete geometry. The first chapter is an introduction to the main concepts and properties of lattices. In the second chapter we discuss the sphere packing density problem, its importance and the difficulty in finding denser packings. Examples of lattices with maximum density are analyzed for lower dimensions. In the third chapter we detail the proof of the theorem of Min-kowski - Hlawka which provides a lower bound for lattice packing density of lattices in any dimension. We also present the problem of the fat struts which comes from communication theory and is related to the search for denser projection lattices
ASSUNTO(S)
sphere packings lattice theory empacotamento de esferas teoria dos reticulados geometria de numeros geometry of numbers
