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]
Leer más >
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]
< Leer menos
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Idioma
en
Document de travail - Pré-publication
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
chromatic numbers
parallelohedra
distance graphs
lattices
Orígen
Importado de HalCentros de investigación