{"title":"The Cyclic Groups Generated by Catalan Matrices","authors":"Phichet Jitjankarn, S. Wananiyakul","doi":"10.35834/2021/3301001","DOIUrl":null,"url":null,"abstract":"Let $n$ a be positive integer. The Catalan matrix of order $n$, denoted by $\\mathscr{C}_n[x]$, is a lower triangular Toeplitz matrix whose nonzero elements are expressions containing Catalan numbers and a real parameter $x$. In this paper, we investigate the multiplicative order of the cyclic group generated by $\\mathscr{C}_n[x]$ (for $x\\in\\mathbb{N}$) modulo a positive integer $m$.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Missouri Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35834/2021/3301001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $n$ a be positive integer. The Catalan matrix of order $n$, denoted by $\mathscr{C}_n[x]$, is a lower triangular Toeplitz matrix whose nonzero elements are expressions containing Catalan numbers and a real parameter $x$. In this paper, we investigate the multiplicative order of the cyclic group generated by $\mathscr{C}_n[x]$ (for $x\in\mathbb{N}$) modulo a positive integer $m$.
期刊介绍:
Missouri Journal of Mathematical Sciences (MJMS) publishes well-motivated original research articles as well as expository and survey articles of exceptional quality in mathematical sciences. A section of the MJMS is also devoted to interesting mathematical problems and solutions.