3 papers
math.CO2018
Constructions for the Elekes-Szabó and Elekes-Rónyai problems
Mehdi Makhul, Oliver Roche-Newton, Audie Warren +1
We give a construction of a non-degenerate polynomial and a set of cardinality such that $\left|Z(F)\cap (A \times A \times A) \right| \gg n^{\frac{…
math.CO2018
Ordinary lines in space
Frank de Zeeuw
We prove that if a finite point set in real space does not have too many points on a plane, then it spans a quadratic number of ordinary lines. This answers the real case of a ques…
math.CO2018
Spanned lines and Langer's inequality
Frank de Zeeuw
We collect some results in combinatorial geometry that follow from an inequality of Langer in algebraic geometry. Langer's inequality gives a lower bound on the number of incidence…