{"title":"A study of the k-step generalized balancing sequences","authors":"E. K. Çetinalp, O. Deveci, N. Yilmaz","doi":"10.31926/but.mif.2023.3.65.1.7","DOIUrl":null,"url":null,"abstract":"In this paper, firstly, we define the k-step generalized Balancing sequences and study the Binet formula of these sequences. Also, we find families of super-diagonal matrices such that the permanents of these matrices are the elements of the k-step generalized Balancing sequences. Finally, we examine the periods of the k-step Balancing sequences in the semi-direct product presented by G = < x, y | x2m−1 = y2 = 1, yxy = x−1 > for the generating pair (x, y).","PeriodicalId":53266,"journal":{"name":"Bulletin of the Transilvania University of Brasov Series V Economic Sciences","volume":"72 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Transilvania University of Brasov Series V Economic Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31926/but.mif.2023.3.65.1.7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, firstly, we define the k-step generalized Balancing sequences and study the Binet formula of these sequences. Also, we find families of super-diagonal matrices such that the permanents of these matrices are the elements of the k-step generalized Balancing sequences. Finally, we examine the periods of the k-step Balancing sequences in the semi-direct product presented by G = < x, y | x2m−1 = y2 = 1, yxy = x−1 > for the generating pair (x, y).
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