Counting the number of elements in the mutation classes of \tilde{A}_n-quivers

Abstract

In this article we prove explicit formulae for the number of non-isomorphic cluster-tilted algebras of type \tilde{A}_n in the derived equivalence classes. In particular, we obtain the number of elements in the mutation classes of quivers of type \tilde{A}_n. As a by-product, this provides an alternative proof for the number of quivers of Dynkin type D_n which was first determined by Buan and Torkildsen.

17 pages. v2: new coauthor, main result strongly improved; v3: minor clarifications

References in corpus (1)

• Counting cluster-tilted algebras of type $A_n$

Cited by in corpus (2)

• A compendium on the cluster algebra and quiver package in sage
• Coloured quivers of type A and the cell-growth problem