Minimal right determiners of irreducible morphisms in algebras of type An

Let Λ be a finite dimensional algebra of type An over a field with the quiver Q and let |Det(Λ)| be the number of the minimal right determiners of all irreducible morphisms between indecomposable left Λ-modules. If Λ is a path algebra, then we have|Det(Λ)|={2n−2,if p=0;2n−p−1,if p≥1, where p=|{i|i is a source in Q with 2≤i≤n−1}|. If Λ is a bound quiver algebra, then we have|Det(Λ)|={2n−2,if r=1;2n−p−q−1,if r≥2, where q is the number of non-zero sink ideals of Λ and r=|{i|i is a sink in Q with 1≤i≤n}|.