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Hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas Quaternions with it’s associated Spinor algebra | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 شهریور 1403 اصل مقاله (406.72 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29372.1966 | ||
| نویسندگان | ||
| Ritanjali Mohanty؛ Hrishikesh Mahato* | ||
| Department of Mathematics, Central University of Jharkhand, India | ||
| چکیده | ||
| In this article, we introduce and study hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas spinors. First, we give hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas quaternions with some algebraic properties. Next we introduce the spinor family of $k$-Mersenne and $k$-Mersenne-Lucas numbers using the hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas quaternions. Here, we start with Binet-type formulas and algebraic properties such as Catalan's identity, Cassini's identity, d'Ocagne's identity, etc. Additionally, we obtain various types of generating functions. Moreover, we give partial sum formulas in closed form. | ||
| کلیدواژه‌ها | ||
| Hyperbolic k-Mersenne quaternions؛ Hyperbolic k-Mersenne Spinors؛ Binet Formula؛ Catalan Identity؛ Generating Function | ||
| مراجع | ||
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[1] É. Cartan, The Theory of Spinors, Courier Corporation, 2012.
[2] G.F.T. Castillo, 3-D Spinors, Spin-Weighted Functions and their Applications, Birkhauser Boston, MA, 2012.
[3] M. Chelgham and A. Boussayoud, On the $k$-Mersenne–Lucas numbers, Notes Number Theory Discrete Math. 27 (2021), no. 1, 7–13. http://doi.org/10.7546/nntdm.2021.27.1.7-13 [4] T. Eri̇şi̇r and M.A. Güngör, On fibonacci spinors, Int. J. Geom. Methods Mod. Phys. 17 (2020), no. 4, Article ID: 2050065. https://doi.org/10.1142/S0219887820500656 [5] S. Falcon and Á. Plaza, The $k$-Fibonacci sequence and the Pascal 2-triangle, Chaos Solit. Fractals 33 (2007), no. 1, 38–49. https://doi.org/10.1016/j.chaos.2006.10.022 [6] M. Kumari, K. Prasad, and R. Frontczak, On the $k$-Fibonacci and $k$-Lucas spinors, Notes Number Theory Discrete Math. 29 (2023), no. 2, 322–335. https://doi.org/10.7546/nntdm.2023.29.2.322-335 [7] A. Macfarlane, Hyperbolic quaternions, Proc. Roy. Soc. Edinburgh Sect. A 23 (1902), 169–180. https://doi.org/10.1017/S0370164600010385 [8] K. Uslu and V. Deniz, Some identities of $k$-Mersenne numbers., Adv. Appl. Discrete Math. 18 (2017), no. 4, 413–423. https://doi.org/10.17654/DM018040413 [9] M.D. Vivarelli, Development of spinor descriptions of rotational mechanics from Euler’s rigid body displacement theorem, Celestial Mech. 32 (1984), no. 3, 193–207. https://doi.org/10.1007/BF01236599 | ||
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