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We derive new upper bounds for the densities of measurable sets in $ℝ^{n}$ which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new upper bounds for measurable sets which avoid the unit distance in dimensions $2, \dots, 24$ . This gives new lower bounds for the measurable chromatic number in dimensions $3, \dots, 24$ . We apply it to get a short proof of a variant of a recent result of Bukh which in turn generalizes theorems of Furstenberg,...

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Finite and infinite packings.

Finite and Uniform Stability of Sphere Coverings.

Finite Coverings by Translates of Centrally Symmetric Convex Domains.

Finite Sphere Packing and Sphere Covering.

Finite sphere packings and critical radii.

Fourier analysis, linear programming, and densities of distance avoiding sets in ℝ n

Currently displaying 1 – 6 of 6

Fourier analysis, linear programming, and densities of distance avoiding sets in $ℝ^{n}$