标题： Kauffman括号多项式，完美匹配和簇变量 显示英文标题

标题： Kauffman bracket polynomials, perfect matchings and cluster variables

摘要： 我们引入了一类链，其括号多项式可以展开为平面二部图的完美匹配。 此类包括2-bridge链、pretzel链和Montesinos链。 我们的第一个主要结果（定理A）部分回答了Kauffman提出的问题，关于琼斯多项式的跨度树展开与钟定理之间的联系。 在定理A的基础上，我们将我们的框架应用于簇理论，并在定理B中证明，此类链的括号多项式可以作为某些簇变量的F多项式的特例。 定理B推广了几项早期的结果。 我们还提出了几个应用和示例。 显示英文摘要

摘要： We introduce a class of links whose bracket polynomials admit an expansion over perfect matchings of a plane bipartite graph. This class includes 2-bridge links, pretzel links, and Montesinos links. Our first main result (Theorem A) provides a partial answer to a question posed by Kauffman concerning the connection between spanning tree expansions of the Jones polynomial and the Clock Theorem. Building on Theorem A, we apply our framework to cluster theory and prove in Theorem B that the bracket polynomials of links in this class can be realized as specializations of the F-polynomials of certain cluster variables. Theorem B generalizes several earlier results. We also present several applications and illustrative examples.