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Optimum basis of finite convex geometry
[article]
2016
arXiv
pre-print
Convex geometries form a subclass of closure systems with unique criticals, or UC-systems. We show that the F-basis introduced in [1] for UC-systems, becomes optimum in convex geometries, in two essential parts of the basis: right sides (conclusions) of binary implications and left sides (premises) of non-binary ones. The right sides of non-binary implications can also be optimized, when the convex geometry either satisfies the Carousel property, or does not have D-cycles. The latter
arXiv:1205.3236v5
fatcat:t2aay3p52nbotgpsjspjmtkflq