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



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Luzón, Ana and 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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Official URL: http://www.sciencedirect.com/science/article/pii/S0166218X07004969


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.

Item Type:Article
Uncontrolled Keywords:Inverse relations; arrays; Banach's fixed point theorem; Pascal triangles; ultrametrics; Riordan arrays; Riordan group; arithmetical triangles
Subjects:Sciences > Mathematics > Group Theory
Sciences > Mathematics > Topology
ID Code:15172
Deposited On:10 May 2012 08:33
Last Modified:12 Dec 2018 15:13

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