Some results about linear recurrence relation homomorphisms

Alexandre Laugier and Manjil P. Saikia
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 4, Pages 58–68
Full paper (PDF, 192 Kb)

Details

Authors and affiliations

Alexandre Laugier
Lycée professionnel Tristan Corbière
16 rue de Kervéguen – BP 17149 – 29671 Morlaix Cedex, France

Manjil P. Saikia
The Abdus Salam International Centre for Theoretical Physics
Strada Costiera-11, Miramare, I-34151, Trieste, Italy

Abstract

In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results associated with them.

Keywords

• k-th order of recurrence relations
• Recurrence relation homomorphisms
• Strong divisibility sequences
• Periodic sequences

AMS Classification

• 11B37
• 11B50

References

1. Apostol, T. M., An Introduction to the Analytic Theory of Numbers, Springer–Verlag, 1975.
2. Chartrand, G., P. Zhang, Discrete Mathematics, Waveland Press, 2011.
3. Gandhi, K. R., Divisibility properties of Fibonacci numbers, South Asian J. Math., Vol. 1, 2011, No. 3, 140–144.
4. Laugier, A., M. P. Saikia, Some properties of Fibonacci numbers, submitted for publication.