Walks on directed graphs and matrix polynomials

Abstract:

We give a matrix generalization of the family of exponential polynomials in one variable φk(x). Our generalization consists of a matrix of polynomials Φk(X)=(Φ(k)i, j(X))ni, j=1 depending on a matrix of variables X=(xi, j)ni, j=1. We prove some identities of the matrix exponential polynomials which generalize classical identities of the ordinary exponential polynomials. We also introduce matrix generalizations of the decreasing factorial (x)k=x(x-1)(x-2)...(x-k+1), the increasing factorial (x)(k)=x(x+1)(x+2)...(x+k-1), and the Laguerre polynomials. These polynomials have interesting combinatorial interpretations in terms of different kinds of walks on directed graphs. © 2000 Academic Press.

Año de publicación:

2000

Keywords:

• Umbral calculus; polynomials of binomial type; walks; digraphs

Fuente:

scopus