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تسجيل مستخدم جديدDescription of closure operators in convex geometries of segments on a line
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Convex geometry is a closure space $(G,phi)$ with the anti-exchange property. A classical result of Edelman and Jamison (1985) claims that every finite convex geometry is a join of several linear sub-geometries, and the smallest number of such sub-geometries necessary for representation is called the convex dimension. In our work we find necessary and sufficient conditions on a closure operator $phi$ of convex geometry $(G,phi)$ so that its convex dimension equals 2, equivalently, they are represented by segments on a line. These conditions can be checked in polynomial time in two parameters: the size of the base set $|G|$ and the size of the implicational basis of $(G,phi)$.
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