On the k-Fibonacci and k-Lucas spinors

Munesh Kumari, Kalika Prasad and Robert Frontczak
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 2, Pages 322–335
DOI: 10.7546/nntdm.2023.29.2.322-335
Full paper (PDF, 285 Kb)

Details

Authors and affiliations

Munesh Kumari
Department of Mathematics, Central University of Jharkhand
Ranchi 835205, India

Kalika Prasad
Department of Mathematics, Central University of Jharkhand
Ranchi 835205, India

Robert Frontczak
Landesbank Baden-Württemberg (LBBW)
Am Hauptbahnhof 2, 70173 Stuttgart, Germany

Abstract

In this paper, we introduce a new family of sequences called the k-Fibonacci and k-Lucas spinors. Starting with the Binet formulas we present their basic properties, such as Cassini’s identity, Catalan’s identity, d’Ocagne’s identity, Vajda’s identity, and Honsberger’s identity. In addition, we discuss their generating functions. Finally, we obtain sum formulae and relations between k-Fibonacci and k-Lucas spinors.

Keywords

• k-Fibonacci spinor
• k-Lucas spinor
• Binet form
• Catalan’s identity
• Generating function

2020 Mathematics Subject Classification

• 15A66
• 11B39
• 11R52

References

1. Cartan, É. (1981). The Theory of Spinors. New York: Dover Publications.
2. Castillo, G. F. T. (2003). 3-D Spinors, Spin-Weighted Functions and Their Applications. Springer Science & Business Media, Vol. 32.
3. Erişir, T., & Güngör, M. A. (2020). On Fibonacci spinors. International Journal of Geometric Methods in Modern Physics, 17, Article 2050065.
4. Falcón, S. (2011). On the 𝑘-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6, 1039–1050.
5. Falcón, S., & Plaza, Á. (2007). On the Fibonacci 𝑘-numbers. Chaos, Solitons & Fractals, 32, 1615–1624.
6. Falcón, S., & Plaza, Á. (2007). The 𝑘-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons & Fractals, 33, 38–49.
7. Ramírez, J. L. (2015). Some combinatorial properties of the 𝑘-Fibonacci and the 𝑘-Lucas quaternions. Analele Stiintifice ale Universitatii Ovidius Constanta Seria Matematica, 23, 201–212.
8. Vivarelli, M. D. (1984). Development of spinor descriptions of rotational mechanics from Euler’s rigid body displacement theorem. Celestial Mechanics, 32, 193–207.

Manuscript history

• Received: 15 September 2022
• Revised: 17 April 2023
• Accepted: 8 May 2023
• Online First: 9 May 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).