Naslov
Symmetric Delone subdivisions and their application.

Autori
Schuermann, Achill ; Dutour Sikirić, Mathieu ; Vallentin, Frank

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
AMS Special Session on Recent Trends in Convex and Discrete Geometry / - , 2006

Skup
AMS Special Session on Recent Trends in Convex and Discrete Geometry

Mjesto i datum
San Antonio (TX), Sjedinjene Američke Države, 12.01.2006. - 16.01.2006

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Delaunay subdivizion; L-type; enumeration

Sažetak
A classical topic in Discrete Geometry with various applications to other fields are Delone subdivisions of discrete point sets. In two classical papers, Voronoi developed a theory of L- types, which classifies geometric lattices in d- dimensional Euclidean spaces according to their Delone subdivision or Dirichlet-Voronoi cell respectively. For a given dimension d such a classification can theoretically be used to solve the lattice covering problem. This is impratical though for d ≥ 6. We therefore describe an extension of the classical theory, which enables us to classify Delone subdivisions with certain prescribed properties. Using convex optimization techniques, we apply the new theory to compute various new best known covering lattices. Moreover, we show how to use the theory to obtain a complete classification of totally real thin number fields.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA