Perrin Octonions and Perrin Sedenions

Year 2020, Volume: 8 Issue: 2, 384 - 390, 27.10.2020

Yasemin Taşyurdu Ayşe Akpınar

Abstract

In this study, we introduce new classes of octonion and sedenion numbers associated with Perrin numbers. We define Perrin octonions and Perrin sedenions by using the Perrin numbers. We give some relationship between Perrin octonions, Perrin sedenions and Perrin numbers. Moreover we obtain the generating functions, Binet formulas and sums formulas of them.                                                                                                                                                                                                                                                                       

Keywords

Perrin numbers, Perrin octonions, Perrin sedenions

References

• [1] I. Akkus and O. Kecilioglu, Split Fibonacci and Lucas octonions. Adv. Appl. Clifford Algebras Vol.25, No.3 (2015), 517–525.
• [2] J. Baez, The octonions, Bull. Amer. Math. Soc. Vol.39 No.2 (2002), 145-205.
• [3] G. Bilgici, U. Tokes¸er and Z. U¨ nal, Fibonacci and Lucas Sedenions. J. Integer Seq., Vol.20, 17.1.8, (2017), 11p.
• [4] P. Catarino, k-Pell-Lukas and Modified k-Pell sedenions. Asian-Eur. J. Math. (2018), S1793557119500189.
• [5] R. E. Cawagas, On the structure and zero divisors of the Cayley-Dickson sedenion algebra, Discuss. Math. Gen. Algebra Appl., Vol.24, (2004), 251–265.
• [6] K. Imaeda and M. Imaeda, Sedenions: algebra and analysis, Applied Mathematics and Computation, Vol.115, (2000), 77-88.
• [7] O. Kecilioglu and I. Akkus, The Fibonacci octonions, Adv. Appl. Clifford Algebra, Vol.25, (2015), 151–158.
• [8] R. Serodio, On octonionic polynomials. Adv. Appl. Clifford Algebras Vol.17, No.2 (2007), 245–258.
• [9] A. G. Shannon, P. G. Anderson, and A. F. Horadam, Properties of Cordonnier, Perrin and van der laan numbers, International Journal of Mathematical Education in Science and Technology, Vol.37, No.7 (2006), 825-831.
• [10] Y. Tasyurdu and A. Akpınar, Padovan and Pell-Padovan Octanions. Turk. J. Math. Comput. Sci., Vol.11(Special Issue), (2019), 114–222.
• [11] Y. Tian, Matrix representations of octonions and their applications. Adv. Appl. Clifford Algebras Vol.10, No.1 (2000), 61–90.