An introduction to the algebraic structure of the Riordan group

• Luis Felipe Prieto Martínez ^[1]
  1. [1] Universidad Politécnica de Madrid

     Universidad Politécnica de Madrid

     Madrid, España

     
• Localización: Pensamiento Matemático, ISSN-e 2174-0410, Vol. 16, Nº. 1, 2026
• Idioma: inglés
• Títulos paralelos:
  • Una introducción a la estructura algebraica del grupo de Riordan
• Enlaces
  • Texto completo
• Resumen
  • español

    This article is an introduction to the Riordan group. It presents, in a self-contained and coherent manner, the foundations for studying its algebraic properties and aims to convey the significance and appeal of such a study.

    It includes the basic definitions and properties of formal power series, the statements and proofs of the two Fundamental Theorems of Riordan Matrices, and the proof that the set of all Riordan matrices indeed forms a group. Finally, the structure of the Riordan group is described as the inverse limit of an inverse sequence of finite-dimensional matrix groups together with a general strategy that made it possible to prove, in a unified way, many recent theorems concerning the algebraic structure of the Riordan group, some of which are listed at the end of the article.

  • English

    Este artículo es una introducción al grupo de Riordan. Presenta, de forma autocontenida y coherente, los fundamentos para el estudio de sus propiedades algebraicas e intenta transmitir el interés que tiene dicho estudio.

    Se incluyen las definiciones y propiedades básicas sobre series formales de potencias, el enunciado y la demostración de los dos Teoremas Fundamentales de las Matrices de Riordan y la demostración de que el conjunto de todas las matrices de Riordan es, efectivamente, un grupo. Finalmente, se describe la estructura del grupo de Riordan como límite inverso de una sucesión inversa de grupos de matrices de dimensión finita y una estrategia general que ha permitido demostrar, de forma unificada, muchos teoremas recientes sobre la estructura algebraica del grupo de Riordan, algunos de los cuales se listan al final del artículo.

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