The main objects of our study are the algebraic structure of Riordan arrays, the properties of subgroups of the Riordan group and relationships among directly related or unrelated theories and objects. Firstly, we introduce formal power series, generating functions and their links to lattice paths and continued fractions. We then present the Riordan group, focusing on the important Riordan subgroups and extending the related theory. These results lead us to the study of quasi-involutions, a special type of Riordan arrays, that we link it to a form of orthogonal polynomials. In the following chapter, we present our findings in the theory of almost-Riordan arrays, a newly discovered type of Riordan arrays. In the final chapter, we concern ourselves with the Linear Algebra of Riordan arrays and their analysis through their eigenvalues and eigenvectors.
|Publication status||Unpublished - 2020|
- Riordan Arrays