On k-Fibonacci hybrid numbers and their matrix representations

Fügen Torunbalcı Aydın
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 257–266
DOI: 10.7546/nntdm.2021.27.4.257-266
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Authors and affiliations

Fügen Torunbalcı Aydın
Yildiz Technical University, Faculty of Chemical and Metallurgical Engineering
Department of Mathematical Engineering
Davutpasa Campus, 34220, Esenler, Istanbul, Turkey

Abstract

In this paper, k-Fibonacci hybrid numbers are defined. Also, some algebraic properties of k-Fibonacci hybrid numbers such as Honsberger identity, Binet Formula, generating functions, d’Ocagne identity, Cassini and Catalan identities are investigated. In addition, we also give 2 × 2 and 4 × 4 representations of the k-Fibonacci hybrid numbers HF_k,n.

Keywords

• Hybrid number
• k-Fibonacci number
• k-Fibonacci hybrid number
• k-Fibonacci number hybrid matrix

2020 Mathematics Subject Classification

• 11B37
• 11B39
• 11B50
• 11C20
• 15A33

References

1. Aydın Torunbalcı, F. (2018). The k-Fibonacci Dual Quaternions. International Journal of Mathematical Analysis, 12(8), 363–373.
2. Cakır, H., & Ozdemir, M. (2021). Hybrid Number Matrices. researchgate.net.
3. Cerda-Morales, G. (2018). Investigation of Generalized Hybrid Fibonacci Numbers and Their Properties, ArXiv:1806.02231v1.
4. Falcon, S., & Plaza, A. (2007). On the Fibonacci k-numbers. Chaos Solitons Fractals, 32(5), 1615–1624.
5. Falcon, S., & Plaza, A. (2007). The k-Fibonacci sequence and the Pascal 2-triangle. Chaos Solitons Fractals, 33(1), 38–49.
6. Falcon, S. (2011). On the k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6(21), 1039–1050.
7. Falcon, S. (2016). On the powers of the k-Fibonacci numbers. Ars Combinatoria, 127, 329–338.
8. Falcon, S. (2016). On the complex k-Fibonacci numbers. Cogent Mathematics, 3(1), Article 1201944.
9. Ozdemir, M. (2018). Introduction to Hybrid Numbers. Advances in Applied Clifford Algebras, 28(11), 10–32.
10. Polatlı, E., Kızılates, C., & Kesim, S. (2016). On Split k-Fibonacci and k-Lucas Quaternions. Advances in Applied Clifford Algebras, 26(1), 353–362.
11. Ramirez, J. L. (2015). Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions. Analele Universitatii Ovidius Constanta-Seria Matematica, 23(2), 201–212.