An Improved Constant Factor for the Unit Distance Problem
Péter Ágoston, Dömötör Pálvölgyi · Studia Scientiarum Mathematicarum Hungarica · 2022
We prove that the number of unit distances among n planar points is at most 1.94 • n4/3, improving on the previous best bound of 8 n4/3. We also give better upper and lower bounds for several small values of n. We also prove some variants of the crossing lemma and improve some constant factors.