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

## 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 |
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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 |

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Deposited On: | 10 May 2012 08:33 |

Last Modified: | 06 Feb 2014 10:18 |

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