Stefliuk S. Partition polynomials and their applications.

The dissertation focuses on representing partition polynomials with parafunctions of triangular matrices and investigating their properties. It unifies and systemizes the information on partition polynomials with the help of the calculus of triangular matrixes. This approach makes it possible to build pairs of mutually inverse partition polynomials. In particular, the new classes of partition polynomials containing both known and unknown partition polynomials have been built by representing partition polynomials with parafunctions of inclined triangular matrices.The general theorem on representing partition polynomials has been proved. The bijective connections of partition polynomials with linear recurrence relations have been established. The properties of arithmetic functions which generalize classic arithmetic functions of unordered partitions and sums of positive integer divisors have been studied. A certain modification of the classic theorem on inversion of arithmetic functions has been proposed.