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We interpret the reciprocation process in K[[x]] as a fixed point problem related to contractive functions for certain adequate ultrametric spaces. This allows us to give a dynamical interpretation of certain arithmetical triangles introduced herein. Later we recognize, as a special case of our construction, the so called Riordan group which is a device… (More)

Recently, the concept of the complementary array of a Riordan array (or recursive matrix) has been introduced. Here we generalize the concept and distinguish between dual and complementary arrays. We show a number of properties of these arrays, how they are computed and their relation with inversion. Finally, we use them to find explicit formulas for the… (More)

This paper describes an application of Rota and collaborator's ideas on the foundations on combinatorial theory to the computing of solutions of some linear functional partial differential equations. We give a dynamical interpretation of the convolution families of polynomials as the entries, in the matrix representation, of the exponentials of certain… (More)

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