Super Markov Numbers and Signed Double Dimer Covers

We provide a superalgebraic analogue of Markov numbers, which are defined as the Grassmann integer solutions to the equation $x^2 + y^2 + z^2 + (xy + yz + xz)\epsilon = 3(1 + \epsilon)xyz$, as well as applications to the Decorated Super Teichm\"uller spaces associated to the once-punctured torus and certain annuli. We conclude with further directions for study.