3 papers
math.CO2025
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 ErdÅs, Elekes, Sheffer and Silier, Guth and Silier, and…
math.CO2025
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…
math.CO2024
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…