On cardinality constrained polymatroids

This paper extends results on the cardinality constrained matroid polytope presented in Maurras and Stephan (2011)  [8] to polymatroids and the intersection of two polymtroids. Given a polymatroid Pf(S) defined by an integer submodular function f on some set S and an increasing finite sequence c of natural numbers, the cardinality constrained polymatroid is the convex hull of the integer points x∈Pf(S) whose sum of all entries is a member of c. We give a complete linear description for this polytope, characterize some facets of the cardinality constrained version of Pf(S), and briefly investigate the separation problem for this polytope. Moreover, we extend the results to the intersection of two polymatroids.