# A formula for $F$-Polynomials in terms of $C$-Vectors and Stabilization of $F$-Polynomials

@article{Gupta2018AFF, title={A formula for \$F\$-Polynomials in terms of \$C\$-Vectors and Stabilization of \$F\$-Polynomials}, author={Meghal Gupta}, journal={arXiv: Combinatorics}, year={2018} }

Given a quiver associated to a cluster algebra and a sequence of vertices, iterative mutation leads to $F$-Polynomials which appear in numerous places in the cluster algebraic literature. The coefficients of the monomials in these $F$-Polynomials are difficult to understand and have been an area of study for many years. In this paper, we present a general closed-form formula for these coefficients in terms of elementary manipulations with $C$-matrices. We then demonstrate the effectiveness of…

## 5 Citations

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We characterize the cluster variables of skew-symmetrizable cluster algebras of rank 3 by their Newton polytopes. The Newton polytope of the cluster variable $z$ is the convex hull of the set of all…

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We discuss a product formula for F -polynomials in cluster algebras, and provide two proofs. One proof is inductive and uses only the mutation rule for F polynomials. The other is based on the…

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