Mixed Dimer Configuration Model in Type $D$ Cluster Algebras II: Beyond the Acyclic Case
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 $D_n$ using dimer and double dimer conf...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
15.11.2022
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Subjects | |
Online Access | Get full text |
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Summary: | 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 $D_n$ 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. |
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DOI: | 10.48550/arxiv.2211.08569 |