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] | |
hal.structure.identifier | Reformulations based algorithms for Combinatorial Optimization [Realopt] | |
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 | 2024-04-04T03:09:37Z | |
dc.date.available | 2024-04-04T03:09:37Z | |
dc.date.created | 2017-07-21 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193621 | |
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 Voronoï regions of the lattices An, n >= 2. | |
dc.language.iso | en | |
dc.rights.uri | http://creativecommons.org/licenses/by/ | |
dc.subject.en | chromatic numbers | |
dc.subject.en | parallelohedra | |
dc.subject.en | distance graphs | |
dc.subject.en | lattices | |
dc.title.en | On the density of sets avoiding parallelohedron distance 1 | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Mathématiques [math]/Combinatoire [math.CO] | |
dc.subject.hal | Mathématiques [math]/Géométrie métrique [math.MG] | |
dc.identifier.arxiv | 1708.00291 | |
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-01567118 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-01567118v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BACHOC,%20Christine&BELLITTO,%20Thomas&MOUSTROU,%20Philippe&P%C3%8ACHER,%20Arnaud&rft.genre=preprint |
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