A criterion for the existence and uniqueness of polyorthogonal polynomials of the second type

New concepts are introduced in the work: an admissible index and an almost perfect system of functions. Using these concepts for an arbitrary system of power series of Laurent type a criterion for the uniqueness of an associated with this system of a polyorthogonal polynomial is formulated and proved. The explicit form of this polynomial is found, as well as the explicit form of polynomials standing in the numerator and denominator of the corresponding of Pade approximations. The propositions proved complement the well-known results the in theory of polyorthogonal polynomials and Pade approximations.