The Linear Algebra of (r, β)-Stirling Matrices

IF 1 Q1 MATHEMATICS
Genevieve B. Engalan, Mary Joy Latayada
{"title":"The Linear Algebra of (r, β)-Stirling Matrices","authors":"Genevieve B. Engalan, Mary Joy Latayada","doi":"10.29020/nybg.ejpam.v16i4.4854","DOIUrl":null,"url":null,"abstract":"This paper establishes the linear algebra of the $(r, \\beta)$-Stirling matrix. Along the way, this paper derives various identities, such as its factorization and relationship to the Pascal matrix and the Stirling matrix of the second kind. Additionally, this paper develops a natural extension of the Vandermonde matrix, which can be used to study and evaluate successive power sums of arithmetic progressions.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29020/nybg.ejpam.v16i4.4854","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

This paper establishes the linear algebra of the $(r, \beta)$-Stirling matrix. Along the way, this paper derives various identities, such as its factorization and relationship to the Pascal matrix and the Stirling matrix of the second kind. Additionally, this paper develops a natural extension of the Vandermonde matrix, which can be used to study and evaluate successive power sums of arithmetic progressions.
(r, β)-Stirling矩阵的线性代数
本文建立了$(r, \beta)$-Stirling矩阵的线性代数。在此过程中,本文导出了各种恒等式,如它的因式分解及其与Pascal矩阵和第二类Stirling矩阵的关系。此外,本文还提出了Vandermonde矩阵的一个自然推广,可用于等差数列的连续幂和的研究和求值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信