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arXiv · 2504.11940

$f$-vectors and $F$-invariant in generalized cluster algebras

Huihui Ye·Changjian Fu
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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.

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Huihui Ye, Changjian Fu. 2025-04-16. $f$-vectors and $F$-invariant in generalized cluster algebras. https://arxiv.org/abs/2504.11940

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