# 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:

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