Resumen de The number of generalized balanced lines

David Orden Martín , Pedro Ramos, Gelasio Salazar

• Let S be a set of r red points and b = r+2± blue points in general position in the plane. A line ` determined by them is said to be balanced if in each open half-plane bounded by ` the difference between the number of red points and blue points is ±. We show that every set S as above has at least r balanced lines. The main techniques in the proof are rotations and a generalization, sliding rotations, introduced here.