Isoclasses of iterated tilted algebras of type A_n are in bijection with non-crossing spanning trees of a convex (n+1)-gon up to rotation, giving an explicit count.
Iterated tilted algebras of type
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Enumerating iterated tilted algebras in type $A$
Isoclasses of iterated tilted algebras of type A_n are in bijection with non-crossing spanning trees of a convex (n+1)-gon up to rotation, giving an explicit count.