Luzón, AnaAlonso Morón, Manuel2023-06-202023-06-202008-07-28Luzón, A. y Alonso Morón, M. «Ultrametrics, Banach’s Fixed Point Theorem and the Riordan Group». Discrete Applied Mathematics, vol. 156, n.o 14, julio de 2008, pp. 2620-35. DOI.org (Crossref), https://doi.org/10.1016/j.dam.2007.10.026.0166-218X10.1016/j.dam.2007.10.026https://hdl.handle.net/20.500.14352/49912We 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.engjournal articlehttps//doi.org/10.1016/j.dam.2007.10.026http://www.sciencedirect.com/science/article/pii/S0166218X07004969restricted access512.54515.126.4515.124Inverse relationsArraysBanach's fixed point theoremPascal trianglesUltrametricsRiordan arraysRiordan groupArithmetical trianglesGrupos (Matemáticas)Topología1210 Topología