Half Riordan Array Sequences

Tian-Xiao He

doi:10.1016/j.laa.2020.06.019

Half Riordan Array Sequences

Tian-Xiao He

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

Abstract

We construct sequences of vertical and horizontal halves of various Riordan arrays by using the vertical and horizontal halve Riordan array transform operators. The sequence characterizations of halves of Riordan arrays are presented and applied to the halve Riordan array transformation. The conditions of transforming a Riordan array to a pseudo-involution Riordan array by using the halve Riordan array transform are given. The condition of preserving the elements of a certain subgroup of the Riordan group under the halve Riordan array transformation are shown. Other properties of the halves of Riordan arrays and their entries such as related recurrence relations, double variable generating functions, combinatorial interpretations are also studied.

Original language	American English
Journal	Linear Algebra and Its Applications
Volume	604
DOIs	https://doi.org/10.1016/j.laa.2020.06.019
State	Published - Nov 1 2020

Keywords

A-sequence
B-sequence
Half Riordan arrays
Hitting time Riordan array
Riordan group
Z-sequence

Disciplines

Mathematics
Algebra
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2020.06.019License: Unspecified

Cite this

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title = "Half Riordan Array Sequences",

abstract = " We construct sequences of vertical and horizontal halves of various Riordan arrays by using the vertical and horizontal halve Riordan array transform operators. The sequence characterizations of halves of Riordan arrays are presented and applied to the halve Riordan array transformation. The conditions of transforming a Riordan array to a pseudo-involution Riordan array by using the halve Riordan array transform are given. The condition of preserving the elements of a certain subgroup of the Riordan group under the halve Riordan array transformation are shown. Other properties of the halves of Riordan arrays and their entries such as related recurrence relations, double variable generating functions, combinatorial interpretations are also studied.",

keywords = "A-sequence, B-sequence, Half Riordan arrays, Hitting time Riordan array, Riordan group, Z-sequence",

author = "Tian-Xiao He",

year = "2020",

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doi = "10.1016/j.laa.2020.06.019",

language = "American English",

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journal = "Linear Algebra and Its Applications",

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T1 - Half Riordan Array Sequences

AU - He, Tian-Xiao

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We construct sequences of vertical and horizontal halves of various Riordan arrays by using the vertical and horizontal halve Riordan array transform operators. The sequence characterizations of halves of Riordan arrays are presented and applied to the halve Riordan array transformation. The conditions of transforming a Riordan array to a pseudo-involution Riordan array by using the halve Riordan array transform are given. The condition of preserving the elements of a certain subgroup of the Riordan group under the halve Riordan array transformation are shown. Other properties of the halves of Riordan arrays and their entries such as related recurrence relations, double variable generating functions, combinatorial interpretations are also studied.

AB - We construct sequences of vertical and horizontal halves of various Riordan arrays by using the vertical and horizontal halve Riordan array transform operators. The sequence characterizations of halves of Riordan arrays are presented and applied to the halve Riordan array transformation. The conditions of transforming a Riordan array to a pseudo-involution Riordan array by using the halve Riordan array transform are given. The condition of preserving the elements of a certain subgroup of the Riordan group under the halve Riordan array transformation are shown. Other properties of the halves of Riordan arrays and their entries such as related recurrence relations, double variable generating functions, combinatorial interpretations are also studied.

KW - A-sequence

KW - B-sequence

KW - Half Riordan arrays

KW - Hitting time Riordan array

KW - Riordan group

KW - Z-sequence

UR - https://doi.org/10.1016/j.laa.2020.06.019

U2 - 10.1016/j.laa.2020.06.019

DO - 10.1016/j.laa.2020.06.019

M3 - Article

VL - 604

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Half Riordan Array Sequences

Abstract

Keywords

Disciplines

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