4 papers · 1 filter
More pointsets with many rich lines
Gabriel Currier
We present some new sharp constructions for the Szemerédi-Trotter theorem. These constructions generalize previous work of Erdős, Elekes, Sheffer and Silier, Guth and Silier, and t…
Many unit distances requires many directions
Gabriel Currier, József Solymosi
In this note, we show that in planar pointsets determining many unit distances, these unit distances must span many directions. Specifically, we show that a set of points can d…
On the structure of extremal point-line arrangements
Gabriel Currier, Jozsef Solymosi, Hung-Hsun Hans Yu
In this note, we show that extremal Szemerédi-Trotter configurations are rigid in the following sense: If are sets of points and lines determining at least $C|P|^{2/3}|L|^{2/…
-cluster-free families of subspaces
Gabriel Currier, Shahriar Shahriari
Three -dimensional subspaces , , and of an -dimensional vector space over a finite field are called a -cluster if and ye…