Centralizers of the Riordan Group
Tian-Xiao He, Yuanziyi Zhang
TL;DR
This paper investigates the structure of centralizers within the Riordan group, utilizing Faà di Bruno's formula and A-sequences to characterize Bell and Lagrange type Riordan arrays, with combinatorial and algebraic insights.
Contribution
It introduces a detailed analysis of centralizers in the Riordan group using A-sequences and Faà di Bruno's formula, expanding understanding of their algebraic and combinatorial properties.
Findings
Characterization of centralizers of Bell and Lagrange type Riordan arrays
Application of Faà di Bruno's formula to Riordan arrays
Insights into algebraic and combinatorial structures of the Riordan group
Abstract
In this paper, we discuss centralizers in the Riordan group. We will see that Fa\`a di Bruno's formula is an application of the Fundamental Theorem of Riordan arrays. Then the composition group of formal power series in is studied to construct the centralizers of Bell type and Lagrange type Riordan arrays. Our tools are the -sequences of Riordan arrays and Fa\`a di Bruno's formula. Some combinatorial explanation and discussion about related algebraic topics are also given.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Mathematics and Applications