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The Dodgson/Muir Identity is an identity on determinants of matrix minorsthat generalizes the Dodgson Identity. Using the matrix tree theorem, we createan equivalent forest identity on ordered sets of $k$ forests. We then prove thegeneralized Forest Identity, and by extension the Dodgson/Muir Identity, usingan edge-swapping involution. This algorithm is a generalization of the Red HotPotato algorithm, developed by the author in 2021 to prove the DodgsonIdentity.

Into the Woods: A graph theoretic proof of the Dodgson/Muir identity