Variations on a theme of Kasteleyn, with Application to the Totally Nonnegative Grassmannian

David E Speyer

Abstract


We provide a short proof of a classical result of Kasteleyn, and prove several variants thereof. One of these results has become key in the parametrization of positroid varieties, and thus deserves the short direct proof which we provide.


Keywords


Perfect matchings, Dimers, Determinant, Pfaffian, Kasteleyn, Positroid

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