Journal of Integer Sequences, Vol. 22 (2019), Article 19.8.4

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
1749-016 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,    dvi,    ps,    latex    

(Concerned with sequences A000027 A000079 A000124 A000125 A000127 A000217 A000292 A000384 A000389 A000580 A000582 A001288 A001519 A002492 A002662 A002664 A005408 A005843 A006261 A008859 A008860 A010966 A010968 A014105 A025581 A035039 A035041 A053126 A053127 A053128 A053129 A059993 A060163 A088305 A114284 A116722 A130883 A145018 A152948 A152950 A165747 A167499 A177787 A201347 A220074.)

Received April 2 2019; revised versions received November 4 2019; December 24 2019. Published in Journal of Integer Sequences, December 26 2019.

Return to Journal of Integer Sequences home page