Super Markov Numbers and Signed Double Dimer Covers
Abstract
We provide a superalgebraic analogue of Markov numbers, which are defined as the Grassmann integer solutions to the equation x2 + y2 + z2 + (xy + yz + xz)ε = 3(1 + ε)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.
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