%0 Journal Article
%A Luzón, Ana
%A Morón, Manuel A.
%T Ultrametrics, Banach's fixed point theorem and the Riordan group
%D 2008
%@ 0166-218X
%U https://hdl.handle.net/20.500.14352/49912
%X 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 it special case of our construction, the so-called Riordan group which is a device used in combinatorics. In this manner we give a new and alternative way to construct the proper Riordan arrays. Our point of view allows us to give a natural metric on the Riordan group turning this group into a topological group. This construction allows us to recognize a countable descending chain of normal subgroups.
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