We study f-vectors, which are the maximal degree vectors of F-polynomials in cluster algebra theory. For a cluster algebra of finite type, we find that positive f-vectors correspond with d-vectors, which are exponent vectors of denominators of cluster variables. Furthermore, using this correspondence and properties of d-vectors, we prove that cluster variables in a cluster are uniquely determined by their f-vectors when the cluster algebra is of finite type or rank 2.

中文翻译：

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有限类型或等级2的簇代数中的f-向量和d-向量之间的关系

我们研究f-向量，这是集群代数理论中F-多项式的最大度向量。对于有限类型的簇代数，我们发现正f-向量与d-向量相对应，d-向量是簇变量分母的指数向量。此外，利用这种对应关系和d-向量的性质，我们证明了当簇代数为有限类型或秩2时，簇中的簇变量由其f-向量唯一确定。