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Ultrametrics, Banach's fixed point theorem and the Riordan group


Luzón, Ana y Morón, Manuel A. (2008) Ultrametrics, Banach's fixed point theorem and the Riordan group. Discrete applied mathematics, 156 (14). pp. 2620-2635. ISSN 0166-218X

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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 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.

Tipo de documento:Artículo
Palabras clave:Inverse relations; arrays; Banach's fixed point theorem; Pascal triangles; ultrametrics; Riordan arrays; Riordan group; arithmetical triangles
Materias:Ciencias > Matemáticas > Grupos (Matemáticas)
Ciencias > Matemáticas > Topología
Código ID:15172

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Última Modificación:06 Feb 2014 10:18

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