Square Matrices Generated by Sequences of Riordan Arrays
Ângela Mestre and José Agapito
Centro de Análise Funcional, Estruturas Lineares e Aplicações
Grupo de Estruturas Algébricas, Lineares e Combinatórias
Departamento de Matemática
Faculdade de Cîencias, Universidade de Lisboa
We consider sequences of images of Riordan arrays under some Riordan
group automorphisms introduced by Bacher. We enclose their properties
into several infinite square arrays which turn out to be of combinatorial
interest. To illustrate our approach we consider Cameron and Nkwanta's
sequence of generalized RNA arrays (whose first term is the well-known
Nkwanta RNA array). Although this sequence of generalized RNA arrays was
originally established as a sequence of pseudo-involutions, we show that
it does not contain pseudo-involutions other than Nkwanta's array. We
also show that these arrays are actually images of a new array under
some of Bacher’s automorphisms. We study the combinatorics of some
square matrices related to the generalized RNA arrays and to sequences
of genuine pseudo-involutions generated by Nkwanta's array.
Full version: pdf,
(Concerned with sequences
Received April 2 2019; revised versions received November 4 2019; December 24 2019.
Published in Journal of Integer Sequences,
December 26 2019.
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