Let $\Q$ be the quiver of Dynkin type $\mathbb{ A}_n$ with linear orientation and $A_{ n}=k\Q$. In this paper, we give a complete classification of the silted algebras of type $A_{ n}$ by using the geometric models of gentle algebras. We show that any finite-dimensional algebra is a silted of type $A_{ n}$ if and only if it is a tilted of type $A_{ n}$ or a tilted algebra of type $A_{ m}\times A_{ n-m}$ for any positive integer $1\leq m\leq n-1$. Based on the classification, we obtain a formula for computing the number of silted algebras of type $A_{ n}$.
Categories: math.RT