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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.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPASSUELLO, Alberto
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTHIÉRY, Alain
dc.date.accessioned2024-04-04T03:22:42Z
dc.date.available2024-04-04T03:22:42Z
dc.date.created2014-01-23
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194780
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.title.enTHE DENSITY OF SETS AVOIDING DISTANCE 1 IN EUCLIDEAN SPACE
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01003676
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01003676v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BACHOC,%20Christine&PASSUELLO,%20Alberto&THI%C3%89RY,%20Alain&rft.genre=preprint


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