Deletion-Contraction Duality for Matroids is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a matroid on a finite ground set , and let . Then, as matroids on the ground set , \begin{align } (M \setminus A)^ = M^ / A. \end{align } Equivalently, deletion in a matroid is dual to contraction in the dual matroid. Moreover, as.