Universität zu Köln

Sikiric, Mathieu Dutour, Madore, David A., Moustrou, Philippe and Vallentin, Frank (2021). Coloring the Voronoi tessellation of lattices. J. Lond. Math. Soc.-Second Ser., 104 (3). S. 1135 - 1172. HOBOKEN: WILEY. ISSN 1469-7750

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Abstract

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 behavior 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Sikiric, Mathieu Dutour UNSPECIFIED UNSPECIFIED UNSPECIFIED Madore, David A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Moustrou, Philippe UNSPECIFIED UNSPECIFIED UNSPECIFIED Vallentin, Frank UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-581479
DOI:	10.1112/jlms.12456
Journal or Publication Title:	J. Lond. Math. Soc.-Second Ser.
Volume:	104
Number:	3
Page Range:	S. 1135 - 1172
Date:	2021
Publisher:	WILEY
Place of Publication:	HOBOKEN
ISSN:	1469-7750
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SPHERE PACKING PROBLEM; BOUNDS; CELLS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/58147