Naslov
Lattice Packings and Coverings

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

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

Izvornik
Colloquium of the math. Department of National university of Ireland, Galway / - , 2009

Skup
Colloquium of the math. Department of National university of Ireland, Galway

Mjesto i datum
Galway, Irska, 26.11.2009

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
perfect form; Erdahl cone; eutaxy; design

Sažetak
A family of balls in Euclidean space is called a packing if for any two balls B and B' their interior do not self-intersect. It is called a covering if every point belong to at least one ball. We focus here on packings and coverings for which the calls are of the form x + B(0, R) with x belonging to a lattice L. If L is fixed then we adjust the value of R to a value R0 to find the best packing. Alternatively we can adjust the value of R to a value R1 to find the best covering. This allow us to define the packing density pack(L) and covering density cov(L) of L. The geometry of the function pack on the space of lattices has been elucidated by Minkovski, Voronoi and Ash. They showed that the function pack has no local minimum, that it is a Morse function and they give a characterization of the local maximum in terms of the algebraic notions of perfection and eutaxy. The covering function cov is much more complex. It has local minimum and local maximum and it is not a Morse function. We also characterize the local maximum of the covering density in terms of the corresponding notions of perfection and eutaxy this time for Delaunay polytope.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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