Naslov
Geometry of numbers, equivalent L-type and coverings

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

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

Izvornik
Stochastic Models and Discrete Geometry (2005), The Institute of Statistical Mathematics / - , 2005

Skup
Stochastic Models and Discrete Geometry (2005), The Institute of Statistical Mathematics

Mjesto i datum
Tokyo, Japan, 24.03.2005. - 25.03.2005

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Delaunay polytope; covering; records

Sažetak
Given a lattice L, a polytope P is called a Delaunay polytope if the set of its vertices is S inter L with S being an empty sphere. The set of lattices of R^n corresponds to the cone of positive definite symmetric matrices. If one prescribes the Delaunay polytopes of the lattice, then the corresponding set of matrices is a polyhedral cone called a L-type. A lattice covering is a set of balls x+B(0, R) with x belonging to a lattice L and such that every point belongs to at least one ball. The optimization of the covering density of lattice belonging to a fixed L-type is a semidefinite programming problem. We introduce an equivariant setting for that theory, i.e. we see what happens when one considers lattices invariant under a fixed symmetry group. We do this restriction, since there is too much L-types for dimensions greater than 5. By application of the theory developed, we obtain some record coverings in dimension 6 and above. Then, we show what happens when one consider non-lattice but still periodic sets of the form x0+L, ..., xm+L with L a lattice and xi some points.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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