F-polynomial formula from continued fractions

作者：Rabideau Michelle^*

来源：Journal of Algebra, 2018, 509: 467-475.

DOI：10.1016/j.jalgebra.2018.05.019

• Cluster algebras
• Continued fractions
• Snake graphs
• F-polynomial

For cluster algebras from surfaces, there is a known formula for cluster variables and F-polynomials in terms of the perfect matchings of snake graphs. If the cluster algebra has trivial coefficients, there is also a known formula for cluster variables in terms of continued fractions. In this paper, we extend this result to cluster algebras with principal coefficients by producing a formula for the F-polynomials in terms of continued fractions.

• 出版日期2018-9-1