f-vectors and F-invariant in generalized cluster algebras

2025/04/16 by Huihui Ye, Changjian Fu, Ye, Huihui +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2504.11940

Abstract

We establish certain fundamental properties of f-vectors and F-matrices for generalized cluster algebras, including the initial and final seed mutation formulas, the compatibility property and the symmetry property. Along the way, we also generalize the construction of F-invariant for generalized cluster algebras without assuming positivity and prove certain basic properties.

Related

• F-invariant and E-invariant
• Relation between generalized and ordinary cluster algebras
• Study on cluster algebras via abstract pattern and two conjectures on d-vectors and g-vector
• F-invariant in cluster algebras
• Polytope realization of cluster structures