Representation of Convex Geometries by Convex Structures on a Plane
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Date
2016-05
Authors
Bolat, Madina
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
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.
Description
Keywords
Research Subject Categories, Convex geometries
Citation
Madina 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/123456789/1564