Towards a uniform subword complex description of acyclic finite type cluster algebras

Abstract: It has been established in recent years how to approach acyclic cluster algebras of finite type using subword complexes. In this paper, we continue this study by describing the c- and g-vectors, and by providing a conjectured description of the Newton polytopes of the F-polynomials. In particular, we show that this conjectured description would imply that finite type cluster complexes are realized by the duals of the Minkowski sums of the Newton polytopes of either the F-polynomials, or of the cluster variables, respectively.