polymatroid

The polymatroid defined by a given matroid $(E,r)$ is the set ofall functions $w:E\to ℝ$ such that

$$w(e)\ge 0\mathit{\hspace{1em}\hspace{1em}}\text{for all }e\in E$$

$$\sum _{e\in S}w(e)\le r(S)\mathit{\hspace{1em}\hspace{1em}}\text{for all }S\subset E.$$

Polymatroids are related to the convex polytopes seen in linear programming,and have similar uses.