3 research outputs found
On the density of sets of the Euclidean plane avoiding distance 1
A subset is said to avoid distance if: In this paper we study the number
which is the supremum of the upper densities of measurable
sets avoiding distance 1 in the Euclidean plane. Intuitively, represents the highest proportion of the plane that can be filled by a
set avoiding distance 1. This parameter is related to the fractional chromatic
number of the plane.
We establish that and .Comment: 11 pages, 5 figure
On the density of sets of the Euclidean plane avoiding distance
International audienc
On the density of sets of the Euclidean plane avoiding distance 1
A subset is said to avoid distance if: In this paper we study the number
which is the supremum of the upper densities of measurable
sets avoiding distance 1 in the Euclidean plane. Intuitively, represents the highest proportion of the plane that can be filled by a
set avoiding distance 1. This parameter is related to the fractional chromatic
number of the plane.
We establish that and