Mate Matolcsi

Improved bounds for planar sets avoiding unit distances

A 1-avoiding set is a subset of the Euclidean space that does not contain pairs of points at distance 1. We use a Delsarte-type linear programming bound and harmonic analysis to show that such (measurable) sets in the plane have density smaller than 0.258795. Joint work with T. Keleti, F. M. Oliveira Filho, I. Z. Ruzsa.