Abstract
In this paper, we study the maximal length of maximal green sequences for quivers of type \(\widetilde{{\mathbf {D}}}\) and \(\widetilde{{\mathbf {E}}}\) by using the theory of tilting mutation. We show that the maximal length does not depend on the choice of the orientation and determine it explicitly. Moreover, we give a program which counts all maximal green sequences by length for a given Dynkin/extended Dynkin quiver.
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