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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.03194 |
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| _version_ | 1866910010016006144 |
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| author | Huang, Min Ma, Qiling |
| author_facet | Huang, Min Ma, Qiling |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A mutation invariant for skew-symmetrizable matrices Huang, Min Ma, Qiling Combinatorics Representation Theory 13F60, 15A15 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. |
| title | A mutation invariant for skew-symmetrizable matrices |
| topic | Combinatorics Representation Theory 13F60, 15A15 |
| url | https://arxiv.org/abs/2602.03194 |