论文标题
混合二聚体配置模型在类型$ d $ cluster代数II中
Mixed Dimer Configuration Model in Type $D$ Cluster Algebras II: Beyond the Acyclic Case
论文作者
论文摘要
这是第二和第三作者的混合二聚体配置模型的续集，我们将模型扩展到为包含定向循环的码头工作。也就是说，我们使用二聚体和双二聚体配置扩展了$ f $ -d_n $的$ f $ -polyNomials组合模型。特别是，我们给出了一个理论配方，该配方描述了哪些单元出现在这样的$ f $ - 多项式中，以及一种图理论来确定每个单一元素的系数。为了证明此公式，我们在混合二聚体配置与不可兼容的Jacobian代数模块的子模块的尺寸向量之间提供了明确的培养。
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.
