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

DOI10.1016/j.dam.2007.10.026zbMath1152.54032OpenAlexW2008572073MaRDI QIDQ948683

Ana Luzón, Manuel Alonso-Morón

Publication date: 17 October 2008

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2007.10.026

zbMATH Keywords

Banach's fixed point theoremPascal triangleRiordan groupRiordan arraysultrametricsarithmetical triangles

Mathematics Subject Classification ID

Related Items (20)

Double parameter recurrences for polynomials in bi-infinite Riordan matrices and some derived identities ⋮ Finite and infinite dimensional Lie group structures on Riordan groups ⋮ A formula to construct all involutions in Riordan matrix groups ⋮ Iterative processes related to Riordan arrays: the reciprocation and the inversion of power series ⋮ Left multiplication operators on the Riordan group ⋮ Commutators and commutator subgroups of the Riordan group ⋮ Characteristic curves and the exponentiation in the Riordan Lie group: a connection through examples ⋮ \(q\)-double Riordan matrices ⋮ Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions ⋮ Identities induced by Riordan arrays ⋮ Complementary Riordan arrays ⋮ On Ward's differential calculus, Riordan matrices and Sheffer polynomials ⋮ Riordan arrays and related polynomial sequences ⋮ Self-inverse Sheffer sequences and Riordan involutions ⋮ Recurrence relations for polynomial sequences via Riordan matrices ⋮ Some inverse limit approaches to the Riordan group ⋮ Riordan matrices in the reciprocation of quadratic polynomials ⋮ A characterization of the exponential symmetric Sheffer sequences ⋮ The group generated by Riordan involutions ⋮ Products of Riordan arrays of finite orders

Cites Work

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• The Riordan group
• Pascal triangles, Catalan numbers and renewal arrays
• Underdiagonal lattice paths with unrestricted steps
• Riordan arrays and combinatorial sums
• Inverse relations and Schauder bases
• Waiting patterns for a printer
• Some summation rules related to the Riordan arrays
• Bijections and the Riordan group
• Riordan arrays and the Abel-Gould identity
• Generating trees and proper Riordan arrays
• Decomposition and group theoretic characterization of pairs of inverse relations of the Riordan type
• On Some Alternative Characterizations of Riordan Arrays
• The Fibonacci Numbers: Exposed
• Non-archimedian metrizability of topological groups

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