Classification of silted algebras for two quivers of Dynkin type $\mathbb{A}_{n}$

Abstract: In this paper, we give a complete classification of silted algebras for the quiver $\overrightarrow{\mathbb{A}}{n}$ of type $\mathbb{A}{n}$ with linear orientation and for the quiver obtained from $\overrightarrow{\mathbb{A}}_{n}$ by reversing the arrow at the unique source. Based on the classification, we also compute the number of silted algebras for these two quivers.