Matroid Base Polytope Inequality Description is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a matroid on a finite ground set with rank function , and let be its base polytope. For and , write . Then \begin{align } P B(M)=\{x\in\mathbb R^E : x e\ge 0\text{ for all }e\in E,\ x(A)\le r(A)\text{ for all }A\subset E,\.