O. Silier

collaborators

3 papers

math.CO2023

Structure of cell decompositions in Extremal Szemerédi-Trotter examples

Nets Katz, Olivine Silier

The symmetric case of the Szemerédi-Trotter theorem says that any configuration of $N$ lines and $N$ points in the plane has at most $O (N^{4/3})$ incidences. We describe a recipe i…

math.CO2021

Sharp Szemerédi-Trotter Constructions in the Plane

Larry Guth, Olivine Silier

We present a new family of sharp examples for the Szemerédi-Trotter theorem. These are the first examples not based on a rectangular lattice. We also include an application to the…

math.CO2021

A structural Szemerédi-Trotter Theorem for Cartesian Products

Adam Sheffer, Olivine Silier

We study configurations of $n$ points and $n$ lines that form $Θ (n^{4/3})$ incidences, when the point set is a Cartesian product. We prove structural properties of such configurati…