论文标题
混合二聚体配置模型在类型D集群代数中
Mixed Dimer Configuration Model in Type D Cluster Algebras
论文作者
论文摘要
我们为相关颤动是无环的F-多项式和G向量提供了组合模型。我们的模型利用了二聚体配置和双二聚体配置的组合，我们称为混合二聚体配置。特别是，我们给出了一个理论配方，该配方描述了这种f-多项式中哪些单元出现的内容，以及一种图理论来确定每个单一元素的系数。此外，我们对混合二聚体配置模型进行了加权，该模型给出了相关的G-vector。为了证明这个公式，我们使用组合公式是由于Thao Tran而引起的，并在其组合模型和我们自己的组合模型之间提供了明确的射击。
We give a combinatorial model for F-polynomials and g-vectors for type D cluster algebras where the associated quiver is acyclic. Our model utilizes a combination of dimer configurations and double dimer configurations which we refer to as mixed 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. In addition, we give a weighting on our mixed dimer configuration model that gives the associated g-vector. To prove this formula, we use a combinatorial formula due to Thao Tran and provide explicit bijections between her combinatorial model and our own.
