Representation of Convex Geometries by Convex Structures on a Plane - Bolat, Madina (Nazarbayev University School of Science and Technology, 2016)
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.
Keywords: Research Subject Categories; Convex geometries