TY - JOUR
T1 - Representing finite convex geometries by relatively convex sets
AU - Adaricheva, Kira
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2014/4
Y1 - 2014/4
N2 - 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 finite sub-geometries satisfy the n-Carousel Rule, which is the strengthening of the n-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.
AB - 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 finite sub-geometries satisfy the n-Carousel Rule, which is the strengthening of the n-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.
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U2 - 10.1016/j.ejc.2013.07.012
DO - 10.1016/j.ejc.2013.07.012
M3 - Article
AN - SCOPUS:84889645355
VL - 37
SP - 68
EP - 78
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
ER -