# Are there some relations between F-polynomials and theta functions?

F-polynomials are certain polynomials appears in the expansion formula of a cluster variable, see for example the formula (6.5) in cluster algebras IV. Theta functions in the paper correspond to cluster variables. Are there some relations between F-polynomials and theta functions? Thank you very much.

The cluster variables are a subset of the $$\Theta$$ variables. (More generally, the cluster monomials are a subset of the $$\Theta$$ variables. By definition, a cluster monomial is a monomial of the form $$\prod_{i=1}^n x_i^{a_i}$$ where $$(x_1, \ldots, x_n)$$ is a cluster and the $$a_i$$ are $$\geq 0$$.) The $$F$$-polynomials are related to the $$\Theta$$ variables by a simple change of variable described in Cluster Algebras IV.