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Double Dimer Covers on Snake Graphs from Super Cluster Expansions (2110.06497v2)
Published 13 Oct 2021 in math.CO
Abstract: In a paper, the authors gave combinatorial formulas for the Laurent expansions of super $\lambda$-lengths in a marked disk, generalizing Schiffler's $T$-path formula. In the present paper, we give an alternate combinatorial expression for these super $\lambda$-lengths in terms of double dimer covers on snake graphs. This generalizes the dimer formulas of Musiker, Schiffler, and Williams.
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