On the Density of Sets Avoiding Parallelohedron Distance 1
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BACHOC, Christine | |
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| dc.contributor.author | BELLITTO, Thomas | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MOUSTROU, Philippe | |
| hal.structure.identifier | Reformulations based algorithms for Combinatorial Optimization [Realopt] | |
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| dc.contributor.author | PÊCHER, Arnaud | |
| dc.date.accessioned | 2024-04-04T02:56:10Z | |
| dc.date.available | 2024-04-04T02:56:10Z | |
| dc.date.issued | 2019-10 | |
| dc.identifier.issn | 0179-5376 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192439 | |
| dc.description.abstractEn | The 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 Vorono\"i regions of the lattices An, n >= 2. | |
| dc.description.sponsorship | Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003 | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | Chromatic number | |
| dc.subject.en | Lattices | |
| dc.subject.en | Distance graphs | |
| dc.subject.en | Parallelohedra | |
| dc.title.en | On the Density of Sets Avoiding Parallelohedron Distance 1 | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00454-019-00113-x | |
| dc.subject.hal | Sciences de l'Homme et Société/Sciences de l'information et de la communication | |
| dc.identifier.arxiv | 1708.00291 | |
| bordeaux.journal | Discrete and Computational Geometry | |
| bordeaux.page | 497-524 | |
| bordeaux.volume | 62 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02491098 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02491098v1 | |
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