Double dimer covers on snake graphs from super cluster expansions

Gregg Musiker, Nicholas Ovenhouse, Sylvester W Zhang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)325-381
Number of pages57
JournalJournal of Algebra
StatePublished - Oct 15 2022

Bibliographical note

Funding Information:
The authors would like to thank the support of the NSF grants DMS-1745638 and DMS-1854162 , as well as the University of Minnesota UROP program. We would also like to thank Bruce Sagan for many helpful conversations and Ralf Schiffler for his questions motivating some of this work. Lastly, we thank the referee for their helpful edits to the paper.

Publisher Copyright:
© 2022 Elsevier Inc.


  • Cluster algebras
  • Decorated super-Teichmüller spaces
  • Double dimers
  • Snake graphs


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