The number of elements in the mutation classof a quiver of type Dn

摘要

We show that the number of quivers in the mutation class of a quiver of Dynkintype D_nis given by Σdnφ(n/d)(2dd)/(2n)for n ≥ 5. To obtain this formula, wegive a correspondence between the quivers in the mutation class and certain rootedtrees.