A one-parameter generalization of Pfaffians
classification
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one-parameterpfaffiansproveanalogyclosed-formcondensationcrossingsdefine
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In analogy to the definition of the lambda-determinant, we define a one-parameter deformation of the Dodgson condensation formula for Pfaffians. We prove that the resulting rational function is a polynomial with weights given by the crossings and nestings of perfect matchings and prove several identities and closed-form evaluations.
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