Pregled bibliografske jedinice broj: 1214521
Coloring the Voronoi tessellation of lattices
Coloring the Voronoi tessellation of lattices // Journal of the London Mathematical Society, 104 (2021), 2; 1135-1171 doi:10.1112/jlms.12456 (međunarodna recenzija, članak, znanstveni)
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Naslov
Coloring the Voronoi tessellation of lattices
Autori
Dutour-Sikirić, Mathieu ; Madore, David ; Moustrou, Philippe ; Vallentin, Frank
Izvornik
Journal of the London Mathematical Society (0024-6107) 104
(2021), 2;
1135-1171
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Voronoi polytope ; Coloring ; Optimization
Sažetak
In this paper we define the chromatic number of a lattice: It is the least number of colors one needs to color the interiors of the cells of the Voronoi tessellation of a lattice so that no two cells sharing a facet are of the same color. We compute the chromatic number of the root lattices, their duals, and of the Leech lattice, we consider the chromatic number of lattices of Voronoi's first kind, and we investigate the asymptotic behaviour of the chromatic number of lattices when the dimension tends to infinity. We introduce a spectral lower bound for the chromatic number of lattices in spirit of Hoffman’s bound for finite graphs. We compute this bound for the root lattices and relate it to the character theory of the corresponding Lie groups.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
