On the density of sets avoiding parallelohedron distance 1
BELLITTO, Thomas
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
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Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
BELLITTO, Thomas
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
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
Document de travail - Pré-publication
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 Voronoï regions of the lattices An, n >= 2.< Réduire
Mots clés en anglais
chromatic numbers
parallelohedra
distance graphs
lattices
Origine
Importé de halUnités de recherche