Realization of abstract convex geometries by point configurations, Part 1

The Edelman-Jamison problem is to characterize those abstract convex geometries that are representable by a set of points in the plane. We show that some natural modification of the Edelman-Jamison problem is equivalent to the well known NP-hard order type problem

Realization of abstract convex geometries by point configurations. Part I

The Edelman-Jamison problem is to characterize those abstract convex geometries that are representable by a set of points in the plane. We show that some natural modification of the Edelman-Jamison problem is equivalent to the well known NP-hard order type proble

Representation of Convex Geometries by Convex Structures on a Plane

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

Representation of Convex Geometries by Convex Structures on a Plane

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