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

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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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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0166218X07004969


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Resumen

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
Depositado:10 May 2012 08:33
Última Modificación:06 Feb 2014 10:18

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