Polymatroid

In mathematics, the polymatroid defined by a given matroid $(E,r)$ is the set of all functions

: $w:E omathbb{R}$

such that

: $w(e)ge 0$

for all $ein E$

: $sum_{ein S}w(e)le r(S)$

for all

: $Ssubseteq E;$ .

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

The notion was introduced by Jack Edmonds in 1970. MathSciNet|id=0270945

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