On the Pell p-circulant sequences

Yeşim Aküzüm, Ömür Deveci, and A. G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 91—103
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Authors and affiliations

Yeşim Aküzüm
Dr., Faculty of Science and Letters,
Kafkas University 36100, Turkey

Ömür Deveci
Associate Professor, Faculty of Science and Letters,
Kafkas University 36100, Turkey

A. G. Shannon
Emeritus Professor, Faculty of Engineering & IT,
University of Technology Sydney, 2007, Australia

Abstract

In this paper, we define the generalized Pell p-circulant sequence and the Pell pcirculant sequence by using the circulant matrices which are obtained from the characteristic polynomial of the generalized Pell (p,i)-sequence and then, we obtain miscellaneous properties of these sequences. Also, we consider the cyclic groups which are generated by the generating matrices and the auxiliary equations of the defined recurrence sequences and then, we study the orders of these groups. Furthermore, we extend the Pell p-circulant sequence to groups. Finally, we obtain the lengths of the periods of Pell p-circulant sequences in the semidihedral group SD2m for m ≥ 4 as applications of the results obtained.

Keywords

  • Circulant Matrix
  • Sequence
  • Group
  • Period

AMS Classification

  • 11B50
  • 20F05
  • 15A36
  • 20D60

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Cite this paper

APA

Aküzüm, Y., Deveci, Ö. & Shannon A. G. (2017). On the Pell p-circulant sequences. Notes on Number Theory and Discrete Mathematics, 23(2), 91-103.

Chicago

Aküzüm, Yeşim, Ömür Deveci, and A. G. Shannon. “On the Pell p-circulant Sequences.” Notes on Number Theory and Discrete Mathematics 23, no. 2 (2017): 91-103.

MLA

Aküzüm, Yeşim, Ömür Deveci, and A. G. Shannon. “On the Pell p-circulant Sequences.” Notes on Number Theory and Discrete Mathematics 23.2 (2017): 91-103. Print.

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