Pell–Padovan-circulant sequences and their applications

Ömür Deveci and Anthony G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 23, 2017, Number 3, Pages 100–114
Full paper (PDF, 315 Kb)

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Authors and affiliations

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

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

Abstract

This paper develops properties of recurrence sequences defined from circulant matrices obtained from the characteristic polynomial of the Pell-Padovan sequence. The study of these sequences modulo m yields cyclic groups and semigroups from the generating matrices. Finally, we obtain the lengths of the periods of the extended sequences in the extended triangle groups E(2, n, 2), E(2, 2, n) and E(n, 2, 2) for n ≥ 3 as applications of the results obtained.

Keywords

• Circulant matrix
• Sequence
• Group
• Length

AMS Classification

• 11B50
• 20F05
• 11C20
• 20D60

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