集团展开公式与完美匹配
Cluster expansion formulas and perfect matchings
摘要：
我们研究了主系数系统与未穿孔曲面相关联的簇代数。我们给出了一个直接的公式，在这些集群代数中的集群变量的Laurent多项式展开的完美匹配的某个图$G_{T,γ}$，这是从表面构造的递归胶合的基本件，我们称之为瓷砖。我们还给出了这些Laurent多项式展开式在图$G_{T,γ}$的子图方面的第二个公式。
英文摘要：
We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph $G_{T,γ}$ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula for these Laurent polynomial expansions in terms of subgraphs of the graph $G_{T,γ}$.
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