On Lines, Joints, and Incidences in Three Dimensions (2009)
Elekes, György, Kaplan, Haim, Sharir, Micha
We extend (and somewhat simplify) the algebraic proof technique of Guth and Katz \cite{GK}, to obtain several sharp bounds on the number of incidences between lines and points in three dimensions....
Structural results for planar sets with many similar subsets (2008)
Bernardo M. Ábrego, György Elekes, Silvia Fernández-merchant
Consider a k-element subset P of the plane. It is known that the maximum number of sets similar to P that can be found among n points in the plane is Θ(n2) if and only if the cross ratio of any...
On Combinatorics of Projective Mappings (1998)
We consider composition sets of one-dimensional projective mappings and prove that small composition sets are closely related to Abelian subgroups. 0 Introduction Freiman [5, 6] and Ruzsa [12, 13]...