A COMBINATORIAL APPROACH TO BIORTHOGONAL POLYNOMIALS

Abstract

It is proved that biorthogonal polynomials are characterized by the recurrence relations whose coefficients axe related in a certain way. On the basis of these recurrence relations for biorthogonal polynomials, biorthogonal polynomials are interpreted as weights of sets of certain paths in the line, and the moments of the linear functional involved as weights of sets of certain paths in the plane. This interpretation is a generalization of Viennot's interpretation of general orthogonal polynomials.