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arXiv · 2602.03194

A mutation invariant for skew-symmetrizable matrices

Min Huang·Qiling Ma
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Abstract

Matrix mutation of skew-symmetrizable matrices is foundational in cluster algebra theory. Effective mutation invariants are essential for determining whether two matrices lie in the same mutation class. Casals~\cite{Casals} introduced a binary mutation invariant for skew-symmetric matrices. In this paper, we extend Casals' construction to the skew-symmetrizable setting. When the skew-symmetrizer $d_1,\dots, d_n$ is pairwise coprime, we obtain two distinct extensions of this invariant.

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Min Huang, Qiling Ma. 2026-02-03. A mutation invariant for skew-symmetrizable matrices. https://arxiv.org/abs/2602.03194

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