Applications of Riordan Arrays in the Analysis of Algorithms and Structures

The main focus of this study is the algebraic structure of Riordan arrays, the properties of subgroups of the Riordan group and relationships among directly related or unrelated theories and objects and extending this theory. These results lead us to the study of quasi-involutions, a special type of Riordan arrays, that link to orthogonal polynomials.

Properties of the group structure of Riordan arrays are explored in the PhD thesis and publication named in key findings.

PhD thesis submitted by Nikolas Pantelidis entitled 'A study in Algebraic properties of Riordan arrays'. Research article Algebraic properties of Riordan subgroups, Paul Barry, Aoife Hennessy & Nikolaos Pantelidis.