Bolat, Madina2016-05-312016-05-312016-05Madina Bolat. 2016. Representation of Convex Geometries by Convex Structures on a Plane. School of Science and Technology, Nazarbayev University, Astana, Kazakhstan. http://nur.nu.edu.kz/handle/123456789/1564http://nur.nu.edu.kz/handle/123456789/1564Convex 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.enAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject CategoriesConvex geometriesCapstone Project