Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653742 | European Journal of Combinatorics | 2014 | 11 Pages |
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 nn-dimensional vector space and their finite sub-geometries satisfy the nn-Carousel Rule, which is the strengthening of the nn-Carathéodory property. We also find another property, that is similar to the simplex partition property and independent of 2-Carousel Rule, which holds in sub-geometries of 2-dimensional geometries of relatively convex sets.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Kira Adaricheva,