On Some Algebraic Properties of Hermite–Pade Polynomials

We consider a set of $m$ formal power series in non-negative powers of the variable $1/z$, which are in the "general position". For this set of series and corresponding multiindexes depending on an arbitrary natural $n$, constructions of Hermite-Pade polynomials of the 1st and 2nd types with the following property are given. If $M_1(z)$ and $M_2(z)$ are two polynomial matrices corresponding to Hermite-Pade polynomials of the 1st and 2nd types, then their product is equal to the identity matrix.
The result is motivated by some novel applications of Hermite–Padé polynomials to the investigation of monodromy properties of Fuchsian systems of differential equations.