Centralizers of the Riordan Group

In this paper, we discuss centralizers in the Riordan group. We will see that Faà di Bruno’s formula is an application of the Fundamental Theorem of Riordan arrays. Then the composition group of formal power series in 1 is studied to construct the centralizers of Bell type and Lagrange type Riordan arrays. Our tools are the A -sequences of Riordan arrays and Faà di Bruno’s formula. Some combinatorial explanation and discussion about related algebraic topics are also given.