(Nazarbayev University School of Science and Technology, 2016-05) Bolat, Madina
Convex geometries are closure systems satisfying anti-exchange axiom with
combinatorial properties. Every convex geometry is represented by a convex
geometry of points in n-dimensional space with a special closure operator.
Some convex geometries are represented by circles on a plane. This paper
proves that not all convex geometries are represented by circles on a plane
by providing a counterexample. We introduce Weak n-Carousel rule and
prove that it holds for confgurations of circles on a plane.