Representing finite convex geometries by relatively convex sets
Loading...
Date
2011
Authors
Adaricheva, Kira
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
A closure system with the anti-exchange axiom is called a convex
geometry. One geometry is called a sub-geometry of the other if its closed sets
form a sublattice in the lattice of closed sets of the other. We prove that convex
geometries of relatively convex sets in n-dimensional vector space and their
nite sub-geometries satisfy the n-Carousel Rule, which is the strengthening
of the n-Carath eodory property. We also nd another property, that is similar
to the simplex partition property and does not follow from 2-Carusel Rule,
which holds in sub-geometries of 2-dimensional geometries of relatively convex
sets.
Description
Keywords
Research Subject Categories::MATHEMATICS, finite convex geometries
Citation
Adaricheva Kira; 2011; Representing finite convex geometries by relatively convex sets; arXiv.org