Centralizers of the Riordan Group

Tian-Xiao He; Yuanziyi Zhang

doi:10.1007/s13226-022-00218-9

Centralizers of the Riordan Group

Tian-Xiao He, Yuanziyi Zhang

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

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.

Original language	American English
Journal	Indian Journal of Pure and Applied Mathematics
DOIs	https://doi.org/10.1007/s13226-022-00218-9
State	Published - Jan 2022

Keywords

A-sequence
Bell polynomial
Bell type Riordan arrays
Centralizer
Faà di Bruno’s formula
Formal power series
Fundamental theorem of Riordan arrays
Generalized Riordan array
Generating function
Lagrange type Riordan arrays
Riordan group

Disciplines

Applied Mathematics
Mathematics

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Cite this

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title = "Centralizers of the Riordan Group",

abstract = " In this paper, we discuss centralizers in the Riordan group. We will see that Fa{\`a} di Bruno{\textquoteright}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 Fa{\`a} di Bruno{\textquoteright}s formula. Some combinatorial explanation and discussion about related algebraic topics are also given.",

keywords = "A-sequence, Bell polynomial, Bell type Riordan arrays, Centralizer, Fa{\`a} di Bruno{\textquoteright}s formula, Formal power series, Fundamental theorem of Riordan arrays, Generalized Riordan array, Generating function, Lagrange type Riordan arrays, Riordan group",

author = "Tian-Xiao He and Yuanziyi Zhang",

note = "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 $${{{\mathcal {F}}}}_1$$ F 1 is studied to construct the centralizers of Bell type and Lagrange type Riordan arrays.",

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month = jan,

doi = "10.1007/s13226-022-00218-9",

language = "American English",

journal = "Indian Journal of Pure and Applied Mathematics",

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T1 - Centralizers of the Riordan Group

AU - He, Tian-Xiao

AU - Zhang, Yuanziyi

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PY - 2022/1

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N2 - 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.

AB - 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.

KW - A-sequence

KW - Bell polynomial

KW - Bell type Riordan arrays

KW - Centralizer

KW - Faà di Bruno’s formula

KW - Formal power series

KW - Fundamental theorem of Riordan arrays

KW - Generalized Riordan array

KW - Generating function

KW - Lagrange type Riordan arrays

KW - Riordan group

UR - https://link.springer.com/article/10.1007/s13226-022-00218-9

U2 - 10.1007/s13226-022-00218-9

DO - 10.1007/s13226-022-00218-9

M3 - Article

JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

ER -

Centralizers of the Riordan Group

Abstract

Keywords

Disciplines

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