Geodesic
Mixed dimer configuration model in Type \(D\) cluster algebras. II: Beyond the acyclic case
Libby Farrell1 ; Gregg Musiker1 ; Kayla Wright1
1University of Minnesota
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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This is a sequel to the second and third author's Mixed Dimer Configuration Model in Type D Cluster Algebras where we extend our model to work for quivers that contain oriented cycles. Namely, we extend a combinatorial model for F-polynomials for type D using dimer and double dimer configurations. In particular, we give a graph theoretic recipe that describes which monomials appear in such F-polynomials, as well as a graph theoretic way to determine the coefficients of each of these monomials. To prove this formula, we provide an explicit bijection between mixed dimer configurations and dimension vectors of submodules of an indecomposable Jacobian algebra module.
DOI : 10.37236/12070
Classification : 13F60, 16G20

Libby Farrell  1   ; Gregg Musiker  1   ; Kayla Wright  1

1 University of Minnesota 
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     author = {Libby Farrell and Gregg Musiker and Kayla Wright},
     title = {Mixed dimer configuration model in {Type} {\(D\)} cluster algebras. {II:} {Beyond} the acyclic case},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {4},
     doi = {10.37236/12070},
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Libby Farrell; Gregg Musiker; Kayla Wright. Mixed dimer configuration model in Type \(D\) cluster algebras. II: Beyond the acyclic case. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12070

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