Papers › Into the Woods: A graph theoretic proof of the Dodgson/Muir identity
Into the Woods: A graph theoretic proof of the Dodgson/Muir identity
Melanie Fraser
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The Dodgson/Muir Identity is an identity on determinants of matrix minors that generalizes the Dodgson Identity. Using the matrix tree theorem, we create an equivalent forest identity on ordered sets of k forests. We then prove the generalized Forest Identity, and by extension the Dodgson/Muir Identity, using an edge-swapping involution. This algorithm is a generalization of the Red Hot Potato algorithm, developed by the author in 2021 to prove the Dodgson Identity.
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