Minimal Right Determiners Of Irreducible Morphisms

Let A be a finite dimensional algebra of type An over a field with the quiver Q and let |Det(?)| be the number of the minimal right determiners of all irreducible morphisms between indecomposable left ?-modules.If ? is a path algebra.,then we have where P = |{i | i is a source in Q with 2?i?n-1}|.If A is a bound quiver algebra,then we have where Q is the number of non-zero sink ideals of ? and r = |{i | i is a sink in Q with 1 ?i ? n}|.Let ? be a finite dimensional string algebra over a field with the quiver Q such that the underlying graph of Q is a tree,and let | Det(?)? be as above.Then we have| Det(A)| = 2n-p-q-1.where n the number of vertices in Q,p = {| i is a source in Q with two neighbors}and q is the number of non-zero vertex ideals of ?.