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The generalized Alexander polynomial is an invariant of virtual knots/links up to factors of +/- s and t, as described by Louis Kauffman and David E. Radford in Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links, arXiv:math.GT/0112280.

Under inversion and horizontal mirror images, s goes to
s^{-1} and t goes to t^{-1}. Under vertical mirror
images, s goes to t and t goes to s.