Maximal Elements of Polymatroids on Partially Ordered Sets and an Algorithmic Property of Ordered Matroids on Chain Orders

In this paper we continue the investigation of polymatroids defined on partially ordered sets which was started in ''Structural aspects of ordered polymatroids” (Discrete Applied Mathematics 99 (2000)).The core polytope and the set of maximal elements are investigated. A necessary and sufficient condition concerning the rank function of an ordered polymatroid is derived that both sets of basic elements are equal.A characterization of ordered polymatroids by (unordered) polymatroids is given.Ordered matroids are introduced as a set-theoretic version of ordered polymatroids. An algorithmic property of ordered matroids is discussed