Roel Apfelbaum

collaborators

2 papers

cs.CG2017

The Constant of Proportionality in Lower Bound Constructions of Point-Line Incidences

Roel Apfelbaum

Let $I (n, l)$ denote the maximum possible number of incidences between $n$ points and $l$ lines. It is well known that $I (n, l) = Θ (n^{2/3} l^{2/3} + n + l)$ . Let $c_{SzTr}$ …

cs.CG2010

An Improved Bound on the Number of Unit Area Triangles

Roel Apfelbaum, Micha Sharir

We show that the number of unit-area triangles determined by a set of $n$ points in the plane is $O (n^{9/4 + ε})$ , for any $ε > 0$ , improving the recent bound $O (n^{44/19})$ of Dumitre…