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 | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PASSUELLO, Alberto | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | THIÉRY, Alain | |
| dc.date.accessioned | 2024-04-04T03:22:42Z | |
| dc.date.available | 2024-04-04T03:22:42Z | |
| dc.date.created | 2014-01-23 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194780 | |
| 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.title.en | THE DENSITY OF SETS AVOIDING DISTANCE 1 IN EUCLIDEAN SPACE | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| 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-01003676 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01003676v1 | |
| bordeaux.COinS | ctx_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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