Tilting and cotilting for quivers of type Ãn

Tilting and cotilting modules are classified for the completed path algebra of a quiver of type Ãn with linear orientation. This classification problem arises naturally in the classification of cotilting modules over certain associative algebras (Pacific J. Math. 211 (2003) 41–60). The combinatorics of the collection of all tilting and cotilting modules is described in terms of Stasheff associahedra.