Universidad Complutense de Madrid
E-Prints Complutense

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

Impacto

Downloads

Downloads per month over past year

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

[img] PDF
Restringido a Repository staff only

419kB

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


URLURL Type
http://www.sciencedirect.comPublisher


Abstract

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

Origin of downloads

Repository Staff Only: item control page