The density of sets avoiding distance 1 in Euclidean space
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BACHOC, Christine | |
| hal.structure.identifier | Équipe Théorie des Nombres | |
| dc.contributor.author | PASSUELLO, Alberto | |
| hal.structure.identifier | Équipe Théorie des Nombres | |
| dc.contributor.author | THIERY, Alain | |
| dc.date.accessioned | 2024-04-04T03:19:07Z | |
| dc.date.available | 2024-04-04T03:19:07Z | |
| dc.date.created | 2015-01-29 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194475 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.subject.en | unit distance graph | |
| dc.subject.en | measurable chromatic number | |
| dc.subject.en | theta number | |
| dc.subject.en | linear programming | |
| dc.title.en | The density of sets avoiding distance 1 in Euclidean space | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Géométrie métrique [math.MG] | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.identifier.arxiv | 1401.6140 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00935665 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00935665v1 | |
| bordeaux.COinS | ctx_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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