Valuated delta matroids and principal minors of Hermitian matrices
Nathan Cheung, Tracy Chin, Gaku Liu, Cynthia Vinzant
Source abstract
In this paper we introduce valuated Δ -matroids, a natural generalization of two objects of study in matroid theory: valuated matroids and Δ -matroids. We show that these objects exhibit nice properties analogous to ordinary valuated matroids. We also show that these objects arise as the valuations of principal minors of a Hermitian matrix over a valued field, or equivalently from maximal isotropic subspaces of a space with Hermitian sesquilinear form, generalizing other forms of Δ -matroid representability.
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