A Note on Mutation Equivalence

Siyang Liu () and Jie Pan
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Siyang Liu: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Jie Pan: Department of Mathematics, Faculty of Sciences, University of Sherbrooke, Sherbrooke, QC J1N 3C6, Canada

Mathematics, 2025, vol. 13, issue 3, 1-14

Abstract: We focus on the necessary conditions for two totally sign-skew-symmetric matrices B and B ′ to be mutation equivalent, obtaining two specific conditions: the equality of their column greatest common divisor vectors and the equality of | B | and | B ′ | , up to a relabeling of indices, when both matrices are acyclic. As a byproduct, the former condition confirms a conjecture on cluster automorphisms for totally sign-skew-symmetric cluster algebras.

Keywords: totally sign-skew-symmetric matrix; cluster algebra; cluster automorphism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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