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The density of sets avoiding distance 1 in Euclidean space

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBACHOC, Christine
hal.structure.identifierÉquipe Théorie des Nombres
dc.contributor.authorPASSUELLO, Alberto
hal.structure.identifierÉquipe Théorie des Nombres
dc.contributor.authorTHIERY, Alain
dc.date.accessioned2024-04-04T03:19:07Z
dc.date.available2024-04-04T03:19:07Z
dc.date.created2015-01-29
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194475
dc.description.abstractEnWe improve by an exponential factor the best known asymptotic upper bound for the density of sets avoiding 1 in Euclidean space. This result is obtained by a combination of an analytic bound that is an analogue of Lovasz theta number and of a combinatorial argument involving finite subgraphs of the unit distance graph. In turn, we straightforwardly obtain an asymptotic improvement for the measurable chromatic number of Euclidean space. We also tighten previous results for the dimensions between 4 and 24.
dc.language.isoen
dc.subject.enunit distance graph
dc.subject.enmeasurable chromatic number
dc.subject.entheta number
dc.subject.enlinear programming
dc.title.enThe density of sets avoiding distance 1 in Euclidean space
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Géométrie métrique [math.MG]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
dc.identifier.arxiv1401.6140
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00935665
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00935665v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BACHOC,%20Christine&PASSUELLO,%20Alberto&THIERY,%20Alain&rft.genre=preprint


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