A study of the k-step generalized balancing sequences

Authors

  • E.K. Cetinalp Karamanoglu Mehmetbey University, Turkey
  • O. Deveci Kafkas University, Turkey
  • N. Yilmaz Karamano˘glu Mehmetbey University,

DOI:

https://doi.org/10.31926/but.mif.2023.3.65.1.7

Keywords:

balancing sequence, groups, period, presentation

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).

Author Biographies

E.K. Cetinalp, Karamanoglu Mehmetbey University, Turkey

Department of Mathematics, Kamil ¨Ozdag Science Faculty

O. Deveci, Kafkas University, Turkey

Department of Mathematics, Faculty of Science and Letter

N. Yilmaz, Karamano˘glu Mehmetbey University,

Department of Mathematics, Kamil ¨Ozdag Science Faculty 

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Published

2023-07-03

Issue

Section

MATHEMATICS