Double Dimer Covers on Snake Graphs from Super Cluster Expansions

Understand

In a recent 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.