RT Journal Article
T1 Ultrametrics, Banach's fixed point theorem and the Riordan group
A1 Luzón, Ana
A1 Alonso Morón, Manuel
AB 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.
PB Elsevier
SN 0166-218X
YR 2008
FD 2008-07-28
LK https://hdl.handle.net/20.500.14352/49912
UL https://hdl.handle.net/20.500.14352/49912
LA eng
NO Luzón, A. y Alonso Morón, M. «Ultrametrics, Banach’s Fixed Point Theorem and the Riordan Group». Discrete Applied Mathematics, vol. 156, n.o 14, julio de 2008, pp. 2620-35. DOI.org (Crossref), https://doi.org/10.1016/j.dam.2007.10.026.
NO Directorate General for Higher Education (Portugal)
DS Docta Complutense
RD 14 dic 2025