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Mutation-acyclic quivers are totally proper
Published 26 Sep 2024 in math.RT and math.CO | (2409.17832v1)
Abstract: Totally proper quivers, introduced by S.~Fomin and the author arXiv:2406.03604, have many useful properties including powerful mutation invariants. We show that every mutation-acyclic quiver (i.e., a quiver that is mutation equivalent to an acyclic one) is totally proper. This yields new necessary conditions for a quiver to be mutation-acyclic.
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