Rank Formula for Matroid Deletion and Contraction 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 . Let denote the deletion of and let denote the contraction of , both on the ground set . Then for every subset , \begin{align } r {M \setminus e}(A) = r M(A). \end{align.