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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBACHOC, Christine
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierReformulations based algorithms for Combinatorial Optimization [Realopt]
dc.contributor.authorBELLITTO, Thomas
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMOUSTROU, Philippe
hal.structure.identifierReformulations based algorithms for Combinatorial Optimization [Realopt]
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
dc.contributor.authorPÊCHER, Arnaud
dc.date.accessioned2024-04-04T03:09:37Z
dc.date.available2024-04-04T03:09:37Z
dc.date.created2017-07-21
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193621
dc.description.abstractEnThe maximal density of a measurable subset of R^n avoiding Euclidean distance1 is unknown except in the trivial case of dimension 1. In this paper, we consider thecase of a distance associated to a polytope that tiles space, where it is likely that the setsavoiding distance 1 are of maximal density 2^-n, as conjectured by Bachoc and Robins.We prove that this is true for n = 2, and for the Voronoï regions of the lattices An, n >= 2.
dc.language.isoen
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.subject.enchromatic numbers
dc.subject.enparallelohedra
dc.subject.endistance graphs
dc.subject.enlattices
dc.title.enOn the density of sets avoiding parallelohedron distance 1
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.subject.halMathématiques [math]/Géométrie métrique [math.MG]
dc.identifier.arxiv1708.00291
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01567118
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01567118v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BACHOC,%20Christine&BELLITTO,%20Thomas&MOUSTROU,%20Philippe&P%C3%8ACHER,%20Arnaud&rft.genre=preprint


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