On the Density of Sets Avoiding Parallelohedron Distance 1
PÊCHER, Arnaud
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
< Réduire
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Langue
en
Article de revue
Ce document a été publié dans
Discrete and Computational Geometry. 2019-10, vol. 62, n° 3, p. 497-524
Springer Verlag
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
Chromatic number
Lattices
Distance graphs
Parallelohedra
Project ANR
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Origine
Importé de halUnités de recherche