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dc.contributor.authorDutour Sikirić, Mathieu
dc.contributor.authorMadore, David A.
dc.contributor.authorMoustrou, Philippe
dc.contributor.authorVallentin, Frank
dc.date.accessioned2022-02-24T11:29:59Z
dc.date.available2022-02-24T11:29:59Z
dc.date.issued2021-05-03
dc.description.abstractIn 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.en_US
dc.identifier.citationDutour Sikirić, Madore, Moustrou, Vallentin. Coloring the Voronoi tessellation of lattices. Journal of the London Mathematical Society. 2021;104(3):1135-1171en_US
dc.identifier.cristinIDFRIDAID 1989520
dc.identifier.doihttps://doi.org/10.1112/jlms.12456
dc.identifier.issn0024-6107
dc.identifier.issn1469-7750
dc.identifier.urihttps://hdl.handle.net/10037/24130
dc.language.isoengen_US
dc.publisherWileyen_US
dc.relation.journalJournal of the London Mathematical Society
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/764759/Germany/Mixed-Integer Non-Linear Optimisation Applications/MINOA/en_US
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2021 The Author(s)en_US
dc.titleColoring the Voronoi tessellation of latticesen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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