Two Formulas for F-Polynomials

DOI10.1093/IMRN/RNAD074arXiv2112.11839MaRDI QIDQ6183048

Author name not available (Why is that?)

Publication date: 26 January 2024

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: 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 Fock-Goncharov decomposition of mutations. We conclude by expanding this product formula as a sum and illustrate applications. This expansion provides an explicit combinatorial computation of $F$-polynomials in a given seed that depends only on the $mathbfc$-vectors and $mathbfg$-vectors along a finite sequence of mutations from the initial seed to the given seed.

Full work available at URL: https://arxiv.org/abs/2112.11839

Mathematics Subject Classification ID

Cluster algebras (13F60)

Related Items (1)

On \(F\)-polynomials for generalized quantum cluster algebras and Gupta's formula

This page was built for publication: Two Formulas for F-Polynomials

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6183048)