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

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

2009-06-02

arxiv.org/abs/0906.0487v3

Electron. J. Combin. 18 (2011), no. 1, P98

Mathematics

Combinatorics

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

Scientific paper

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.

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