On bicomplex generalized Tetranacci quaternions

Yüksel Soykan and Erkan Taşdemir
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 3, Pages 163–175
DOI: 10.7546/nntdm.2020.26.3.163-175
Full paper (PDF, 173 Kb)

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Authors and affiliations

Yüksel Soykan
Department of Mathematics, Art and Science Faculty
Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey

Erkan Taşdemir
Pınarhisar Vocational School of Higher Education
Kırklareli University, 39300, Kırklareli, Turkey

Abstract

In this paper, we introduce the bicomplex generalized Tetranacci quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them.

Keywords

• Bicomplex Tetranacci numbers
• Quaternions
• Bicomplex Tetranacci quaternions
• Bicomplex Tetranacci–Lucas quaternions

2010 Mathematics Subject Classification

• 11B39
• 11B83
• 17A45
• 05A15

References

1. Aydın, F. T. (2018). Bicomplex k-Fibonacci Quaternions, arXiv: 1810.05003 [math.NT].
2. Aydın, F. T. (2018). On Bicomplex Pell and Pell–Lucas Numbers, Communications in Advanced Mathematical Sciences, 1 (2), 142–155.
3. Bacani, J. B., & Rabago, J. F. T. (2015). On Generalized Fibonacci Numbers, Applied Mathematical Sciences, 9 (25), 3611–3622.
4. Catarino, P. (2019). Bicomplex k-Pell Quaternions, Computational Methods and Function Theory, 19, 65-76.
5. Cerda, G. (2018). Bicomplex Third-Order Jacobsthal quaternions, arXiv: 1809.06979 [math.AC].
6. Dresden, G.P. & Du, Z. (2014). A Simplified Binet Formula for k-Generalized Fibonacci Numbers, J. Integer Seq., 17, art. 14.4.7, 1–9.
7. Luna-Elizarraras, M.E., Shapiro, M., Struppa, D.C., & Vajiac, A. (2012). Bicomplex Numbers and their Elementary Functions, CUBO A Mathematical Journal, 14 (2), 61–80.
8. Halıcı, S., & Karataş, A. (2018). Bicomplex Lucas and Horadam Numbers, arXiv:
   1806.05038v2 [math.RA].
9. Halici, S. (2019). On Bicomplex Fibonacci Numbers and Their Generalization. In: Flaut C., Hoskova-Mayerova S., Flaut D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, Vol 179. Springer, 509–524.
10. Hathiwala, G.S., & Shah, D.V. (2017). Binet–Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods, Mathematical Journal of Interdisciplinary Sciences, 6 (1), 37–48.
11. Howard, F.T., & Saidak, F. (2010). Zhou’s Theory of Constructing Identities, Congress Numer., 200, 225–237.
12. Kızılateş, C., Catarino, P., & Tuğlu, N. (2019). On the Bicomplex Generalized Tribonacci Quaternions. Mathematics, 7, 80.
13. Melham, R. S. (1999). Some Analogs of the Identity F_n² + F_n+1² = F_2n+1², Fibonacci Quarterly, 37 (4), 305–311.
14. Natividad, L. R. (2013). On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3 (2), 38–40.
15. Nurkan, S.K., & Güven, İ. A. (2015). A Note on Bicomplex Fibonacci and Lucas Numbers, arXiv: 1508.03972 [math.NT].
16. Nurkan, S.K., & Güven İ. A. (2018). A Note on Bicomplex Fibonacci and Lucas Numbers, International Journal of Pure and Applied Mathematics, 120 (3), 365–377.
17. Rochon, D., & Shapiro, M. (2004). On Algebraic Properties of Bicomplex and Hyperbolic Numbers, Anal. Univ. Oradea Fascicola. Matematica, 11, 1–28.
18. Singh, B., Bhadouria, P., Sikhwal, O., & Sisodiya, K. (2014). A Formula for Tetranacci-Like Sequence, Gen. Math. Notes, 20 (2), 136–141.
19. Soykan, Y. (2019). Gaussian Generalized Tetranacci Numbers, Journal of Advances in Mathematics and Computer Science, 31 (3), 1–21.
20. Soykan, Y. (2019). Bicomplex Tetranacci and Tetranacci–Lucas Quaternions, Communications in Mathematics and Applications, 11 (1), 95–112.
21. Waddill, M.E. (1967). Another Generalized Fibonacci Sequence, Fibonacci Quarterly, 5 (3), 209–227.
22. Waddill, M.E. (1992). The Tetranacci Sequence and Generalizations, The Fibonacci Quarterly, 30 (1), 9–20.
23. Zaveri, M.N. & Patel, J.K. (2016). Binet’s Formula for the Tetranacci Sequence, International Journal of Science and Research, 5 (12), 1911–1914.