It is known that there are infinitely many exceptional sequences of quiver representations for Euclidean quivers. In this paper we study those of type Ãn and classify them into finitely many parametrized families. We first give a bijection between exceptional collections and a combinatorial object known as strand diagrams. We will then define parametrized families of exceptional collections and use strand diagrams to show that there are finitely many such families. We moreover show that these families of exceptional collections are in bijection with small strand diagrams. Finally we construct two more combinatorial objects, chord and arc diagrams, that also describe exceptional collections of type Ãn and are in bijection with parametrized families.
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