Abstract
If the collection of all real-valued functions defined on a finite partially ordered set S of n elements is identified in the natural way with R n , it is obvious that the subset of functions that are isotone or order preserving with respect to the given partial order constitutes a closed, convex, polyhedral cone K in R n . The dual cone K * of K is the set of all linear functionals that are nonpositive of K. This article identifies the important geometric properties of K, and characterizes a nonredundant set of defining equations and inequalities for K * in terms of a special class of partitions of S into upper and lower sets. These defining constraints immediately imply a set of extreme rays spanning K and K *. One of the characterizations of K * involves feasibility conditions on flows in a network. These conditions are also used as a tool in analysis.
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