# polymatroid

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

 $w(e)\geq 0\qquad\text{for all }e\in E$
 $\sum_{e\in S}w(e)\leq r(S)\qquad\text{for all }S\subset E\;.$

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

Title polymatroid Polymatroid 2013-03-22 13:56:43 2013-03-22 13:56:43 mathcam (2727) mathcam (2727) 4 mathcam (2727) Definition msc 05B35