Walks on directed graphs and matrix polynomials (Q1584671)

The author considers matrix polynomial generalizations of the following classical families of binomial type: the decreasing factorials, the increasing factorials, the exponential polynomials, and the Laguerre polynomials. The approach adopted here is purely combinatorial, and the four families of matrix polynomials are interpreted in terms of walks on digraphs, and all the proofs of algebraic identities presented are bijective. The recursive formulae given here for the exponential and Laguerre polynomials are natural generalizations of the classical Rodrigues formula.