Double Dimer Covers on Snake Graphs from Super Cluster Expansions

2021/10/13 by Gregg Musiker, Musiker, Gregg, Nicholas Ovenhouse +3
Mathematics · #05C70 #13F60 #17A70 #30F60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05C70 #msc:13F60 #msc:17A70 #msc:30F60

paper · pdf · doi:10.48550/arxiv.2110.06497

Minor edits

openalex publication_date 2021/10/13 · arxiv created 2021/11/17 · arxiv updated 2021/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper, the authors gave combinatorial formulas for the Laurent expansions of super λ-lengths in a marked disk, generalizing Schiffler's T-path formula. In the present paper, we give an alternate combinatorial expression for these super λ-lengths in terms of double dimer covers on snake graphs. This generalizes the dimer formulas of Musiker, Schiffler, and Williams.

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