D型簇代数中的混合二聚体构型模型
Mixed Dimer Configuration Model in Type D Cluster Algebras
摘要：
本文给出了D型簇代数的F-多项式和g-向量的一个组合模型，其中关联的G是非循环的。我们的模型利用了二聚体构型和双二聚体构型的组合，我们称之为混合二聚体构型。特别是，我们给出了一个图形理论的配方，描述了单项式出现在这样的F-多项式，以及图形理论的方式来确定这些单项式的系数。此外，我们给我们的混合二聚体配置模型，给出了相关的g-向量的权重。为了证明这个公式，我们使用的组合公式，由于陶陈和她的组合模型和我们自己之间提供明确的双射。
英文摘要：
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.
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