Relation Between f-Vectors and d-Vectors in Cluster Algebras of Finite Type or Rank 2

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