BACHOC, Christine; BELLITTO, Thomas; MOUSTROU, Philippe; PÊCHER, Arnaud

doi:10.1007/s00454-019-00113-x

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BACHOC, Christine
Institut de Mathématiques de Bordeaux [IMB]

BELLITTO, Thomas
Laboratoire Bordelais de Recherche en Informatique [LaBRI]

MOUSTROU, Philippe
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Este ítem está publicado en

Discrete and Computational Geometry. 2019-10, vol. 62, n° 3, p. 497-524

Springer Verlag

Resumen en inglés

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.< Leer menos

Palabras clave en inglés

Chromatic number

Lattices

Distance graphs

Parallelohedra

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192439

DOI

http://dx.doi.org/10.1007/s00454-019-00113-x

Proyecto ANR

Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

Orígen

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Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251