COUNTING CLUSTER-TILTED ALGEBRAS OF TYPE An

Authors : Hermund André TORKİLDSEN

Pages : 149-158

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Publication Date : 2008-12-01

Article Type : Research Paper

Abstract :The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type An, by counting the mutation class of any quiver with underlying graph An. It will also follow that if T and T0 are cluster-tilting objects in a cluster category C, then EndCinsert ignore into journalissuearticles values(T); is isomorphic to EndCinsert ignore into journalissuearticles values(T0); if and only if T = τiT0.
Keywords : Cluster category, cluster tilted algebra, quiver, mutation, mutation class, triangulation of polygons, Catalan number