On the density of sets avoiding parallelohedron distance 1
Combinatorics
2017-08-02 v1 Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1708.00291,
title = {On the density of sets avoiding parallelohedron distance 1},
author = {Christine Bachoc and Thomas Bellitto and Philippe Moustrou and Arnaud Pêcher},
journal= {arXiv preprint arXiv:1708.00291},
year = {2017}
}