Fuss–Catalan Matrices, Their Weighted Sums, and Stabilizer Subgroups of the Riordan Group

Tian-Xiao He; Louis W. Shapiro

doi:10.1016/j.laa.2017.06.025

Fuss–Catalan Matrices, Their Weighted Sums, and Stabilizer Subgroups of the Riordan Group

Tian-Xiao He, Louis W. Shapiro

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

Abstract

In this paper, we present the Riordan arrays called Fuss–Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss–Catalan numbers. We also discuss weighted sums of the Fuss–Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.

Original language	American English
Journal	Linear Algebra and Its Applications
Volume	532
DOIs	https://doi.org/10.1016/j.laa.2017.06.025
State	Published - Nov 1 2017

Keywords

Catalan numbers
Fundamental theorem of Riordan arrays
Fuss–Catalan matrices
Fuss–Catalan numbers
Generating function
Riordan group
Stabilizer

Disciplines

Applied Mathematics
Mathematics

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10.1016/j.laa.2017.06.025License: Unspecified

Cite this

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title = "Fuss–Catalan Matrices, Their Weighted Sums, and Stabilizer Subgroups of the Riordan Group",

abstract = " In this paper, we present the Riordan arrays called Fuss–Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss–Catalan numbers. We also discuss weighted sums of the Fuss–Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.",

keywords = "Catalan numbers, Fundamental theorem of Riordan arrays, Fuss–Catalan matrices, Fuss–Catalan numbers, Generating function, Riordan group, Stabilizer",

author = "Tian-Xiao He and Shapiro, {Louis W.}",

note = "In this paper, we present the Riordan arrays called Fuss-Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss-Catalan numbers. We also discuss weighted sums of the Fuss-Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.",

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language = "American English",

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T1 - Fuss–Catalan Matrices, Their Weighted Sums, and Stabilizer Subgroups of the Riordan Group

AU - He, Tian-Xiao

AU - Shapiro, Louis W.

N1 - In this paper, we present the Riordan arrays called Fuss-Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss-Catalan numbers. We also discuss weighted sums of the Fuss-Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - In this paper, we present the Riordan arrays called Fuss–Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss–Catalan numbers. We also discuss weighted sums of the Fuss–Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.

AB - In this paper, we present the Riordan arrays called Fuss–Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss–Catalan numbers. We also discuss weighted sums of the Fuss–Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.

KW - Catalan numbers

KW - Fundamental theorem of Riordan arrays

KW - Fuss–Catalan matrices

KW - Fuss–Catalan numbers

KW - Generating function

KW - Riordan group

KW - Stabilizer

UR - https://www.sciencedirect.com/science/article/pii/S0024379517303889

U2 - 10.1016/j.laa.2017.06.025

DO - 10.1016/j.laa.2017.06.025

M3 - Article

VL - 532

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Fuss–Catalan Matrices, Their Weighted Sums, and Stabilizer Subgroups of the Riordan Group

Abstract

Keywords

Disciplines

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