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

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.