A study of the algebraic structure of the Riordan group.

摘要

The purpose of this thesis is to further investigate known facts about the algebraic structure of the Riordan group. Although much combinatorial research has been done with the elements of the Riordan group, few research papers focus exclusively on the algebraic structure of the group. In this paper, we look at some interesting algebraic properties of the Riordan group. For instance, two subgroups, called the power-Bell and the derivative subgroups are discussed. Centralizers, stabilizers and isomorphisms between subgroups are also investigated. An interesting relationship between certain pairs of generating functions that define a stochastic Riordan matrix is also established. This relationship is then used to generate elements of the stochastic subgroup. Finally, a property connecting similar Riordan matrices and Riordan group pseudo-involutions is investigated. As a result of surveying the Riordan group, some known facts are proved in detail and some new properties are obtained.