A note on consistency conditions on dimer models

2010/12/25 by Akira Ishii, Ishii, Akira, Kazushi Ueda +1 · 1 citation
Mathematics · #14D21 #16G20 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1012.5449

openalex publication_date 2010/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We show that for a non-degenerate dimer model, both the first consistency condition of Mozgovoy and Reineke and the properly-orderedness condition of Gulotta are equivalent to a condition on zigzag paths, which goes back to Hanany and Vegh. The last condition is used in arXiv:0905.0059 to study the behavior of a dimer model under the operation of removing a vertex from the lattice polygon and taking the convex hull of the rest.

Citations

• On moduli spaces of quiver representations associated with dimer models

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• Dimer models and exceptional collections
• Inverse algorithm and triple point diagrams

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