polymatroid

The polymatroid defined by a given matroid $(E,r)$ is the set of all 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.

Title	polymatroid
Canonical name	Polymatroid
Date of creation	2013-03-22 13:56:43
Last modified on	2013-03-22 13:56:43
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	4
Author	mathcam (2727)
Entry type	Definition
Classification	msc 05B35