Polymatroid

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Let LaTeX: N be a finite set and let LaTeX: f be a submodular function on the subsets of LaTeX: N with LaTeX: f(\emptyset)=0. The polymatroid associated with LaTeX: (N,f) is the polytope:

LaTeX: 
\left \{x \in \mathbb{R}^{n+}: \sum_{j \in S} x_j \le f(S) \mbox{ for all } S \in N \right \}.


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