Combinatorial Expressions for F-polynomials in Classical Types

TL;DR

This paper provides combinatorial formulas for F-polynomials in classical type cluster algebras using weighted paths, establishing their positivity and offering new computational tools.

Contribution

It introduces explicit combinatorial formulas for F-polynomials in classical types, proving their positivity and enhancing understanding of their structure.

Findings

Explicit combinatorial formulas for F-polynomials

Proof of positivity of F-polynomials in classical types

Enhanced computational methods for cluster algebras

Abstract

We give combinatorial formulas for F-polynomials in cluster algebras of classical types in terms of the weighted paths in certain directed graphs. As a consequence we prove the positivity of F-polynomials in cluster algebras of classical types.