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Perfect forms and the Voronoi algorithm (CROSBI ID 586115)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Dutour Sikirić, Mathieu Perfect forms and the Voronoi algorithm // Colloquium Universität Rostock. 2012

Podaci o odgovornosti

Dutour Sikirić, Mathieu

engleski

Perfect forms and the Voronoi algorithm

The packing problem consists of considering how to pack sphere in Euclidean space with maximal density. The lattice packing problem is the subproblem where one considers the centers of the spheres to be on a lattice. We explain the Gram matrix formalism that allows to reformulate this problem as a matrix problem with the Hermite function. Then we give the definition of Perfect forms and the Voronoi algorithm that allow to enumerate them in small dimension. The full picture is given in dimension 2. Then we explain some extension of the existing theory to Humbert form and to the Rankin constant problem.

lattice; sphere packing; Ryshkov polyhedra; Voronoi algorithm.

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Podaci o prilogu

2012.

objavljeno

Podaci o matičnoj publikaciji

Colloquium Universität Rostock

Podaci o skupu

Colloquium Universität Rostock

ostalo

18.01.2012-18.01.2012

Rostok, Njemačka

Povezanost rada

Matematika