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Article Dans Une Revue Discrete and Computational Geometry Année : 2019

On the Density of Sets Avoiding Parallelohedron Distance 1

Résumé

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.

Dates et versions

hal-02491098 , version 1 (25-02-2020)

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Christine Bachoc, Thomas Bellitto, Philippe Moustrou, Arnaud Pêcher. On the Density of Sets Avoiding Parallelohedron Distance 1. Discrete and Computational Geometry, 2019, 62 (3), pp.497-524. ⟨10.1007/s00454-019-00113-x⟩. ⟨hal-02491098⟩
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