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Mathematics 2019, 7(1), 80; https://doi.org/10.3390/math7010080

On the Bicomplex Generalized Tribonacci Quaternions

1
Department of Mathematics, Faculty of Art and Science, Zonguldak Bülent Ecevit University, 67100 Zonguldak, Turkey
2
Department of Mathematics, University of Trás-os-Montes e Alto Douro, Quinta de Prados, 5001-801 Vila Real, Portugal
3
Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, 06500 Ankara, Turkey
*
Author to whom correspondence should be addressed.
Received: 15 December 2018 / Revised: 7 January 2019 / Accepted: 10 January 2019 / Published: 14 January 2019
(This article belongs to the Section Mathematics and Computers Science)
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Abstract

In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet’s formula, generating functions, and the summation formula for this type of quaternion are given. Lastly, as an application, we present the determinant of a special matrix, and we show that the determinant is equal to the n th term of the bicomplex generalized tribonacci quaternions. View Full-Text
Keywords: bicomplex number; generalized tribonacci sequence; bicomplex generalized tribonacci quaternion bicomplex number; generalized tribonacci sequence; bicomplex generalized tribonacci quaternion
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kızılateş, C.; Catarino, P.; Tuğlu, N. On the Bicomplex Generalized Tribonacci Quaternions. Mathematics 2019, 7, 80.

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