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In this paper, we establish a bijection between the set of mutation classes of mutation-cyclic skew-symmetric integral 3×3−matrices and the set of triples of integers (a, b, c) such that 2 ≤ a ≤ b ≤ c and ab ≥ c. We also give an algorithm allowing to verify whether a matrix is mutation-cyclic or not. We prove that these two cases are not intertwined.
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