Classification of naturally graded nilpotent associative algebras

In the paper, we consider n- dimensional naturally graded nilpotent associative algebras with the characteristic sequence C(A)=(n-m,m) over an algebraically closed field of characteristic zero. There are two types of such algebras. We give the algebraic classification up to isomorphism of both types of algebras. Moreover, we prove that there are no such algebras of the second type for n > 2m+1.