Order polytope

rdf:langString Order polytope

rdf:langString In mathematics, the order polytope of a finite partially ordered set is a convex polytope defined from the set. The points of the order polytope are the monotonic functions from the given set to the unit interval, its vertices correspond to the upper sets of the partial order, and its dimension is the number of elements in the partial order. The order polytope is a distributive polytope, meaning that coordinatewise minima and maxima of pairs of its points remain within the polytope. The order polytope of a partial order should be distinguished from the linear ordering polytope, a polytope defined from a number as the convex hull of indicator vectors of the sets of edges of -vertex transitive tournaments.