Empty red-red-blue triangles

TL;DR

The paper proves a lower bound on the number of empty red-red-blue triangles formed by any balanced bipartition of a general position point set in the plane.

Contribution

It establishes a new combinatorial lower bound of a3(n^{3/2}) for the number of such triangles, advancing understanding of geometric configurations.

Findings

Every balanced bipartition yields a3(n^{3/2}) empty triangles.

The result applies to point sets in general position.

Provides a significant lower bound in geometric combinatorics.

Abstract

Let $P$ be a $2n$-point set in the plane that is in general position. We prove that every red-blue bipartition of $P$ into $R$ and $B$ with $|R| = |B| = n$ generates $\Omega(n^{3/2})$ red-red-blue empty triangles.