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- W2050972008 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 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." @default.
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- W2050972008 date "2014-04-01" @default.
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- W2050972008 title "Representing finite convex geometries by relatively convex sets" @default.
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- W2050972008 doi "https://doi.org/10.1016/j.ejc.2013.07.012" @default.
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