The existence of a maximal Green sequence is not invariant under quiver mutation (Q2629489)

Summary: This note provides a quiver which does not admit a maximal green sequence, but which is mutation-equivalent to a quiver which does admit a maximal green sequence. The proof uses the `scattering diagrams' of \textit{M. Gross} et al. [``Canonical bases for cluster algebras'', Preprint, \url{arXiv:1411.1394}] to show that a maximal green sequence for a quiver determines a maximal green sequence for any induced subquiver.