Article
Centralizers of the Riordan Group
Indian Journal of Pure and Applied Mathematics
(2022)
Abstract
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.
Keywords
- Centralizer,
- Riordan group,
- Formal power series,
- Generalized Riordan array,
- Bell polynomial,
- A-sequence,
- Faà di Bruno’s formula,
- Fundamental theorem of Riordan arrays,
- Bell type Riordan arrays,
- Lagrange type Riordan arrays,
- Generating function
Disciplines
Publication Date
Winter January, 2022
DOI
https://doi.org/10.1007/s13226-022-00218-9
Publisher Statement
The Indian Journal of Pure and Applied Mathematics is published by Springer and the Indian National Science Academy, New Delhi, India. For more information on this journal, please visit the Indian Journal of Pure and Applied Mathematics online.
Citation Information
Tian-Xiao He and Yuanziyi Zhang. "Centralizers of the Riordan Group" Indian Journal of Pure and Applied Mathematics (2022) ISSN: 0019-5588 Available at: http://works.bepress.com/tian_xiao_he/108/