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math.CO — Combinatorics

Complexity of Mutation-Acyclicity and Matrix Mutation Equivalence

Contributed by Qiyue Tang

Mutation-acyclicity of integral skew-symmetrizable matrices belongs to NP. Mutation equivalence belongs to promise-NP when at least one input is mutation-acyclic. For pairs of mutation-cyclic matrices, mutation equivalence is RE-complete and strongly NP-hard. Both results hold even for connected skew-symmetric matrices.

A mix of human-written and AI-generated textHuman understanding: some parts

Nov 07, 202635 pages

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hexagon:2611.00158v1

math.CO — Combinatorics

Undecidability of Quiver Mutation Equivalence

Contributed by Qiyue Tang

We prove that quiver mutation equivalence up to relabeling is undecidable even for one fixed source quiver. We also prove strong NP-hardness.

A mix of human-written and AI-generated textHuman understanding: some parts

Nov 06, 202615 pages

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Complexity of Mutation-Acyclicity and Matrix Mutation Equivalence

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