On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components

Gamaliel Morales

doi:10.47000/tjmcs.1796085

On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components

Abstract

In this study, we introduce a new class of 3-parameter generalized quaternions, whose components are defined using higher order Lichtenberg numbers. These structures, called higher order Lichtenberg 3-parameter generalized quaternions, are investigated from algebraic and analytical perspectives. The study aims to extend the role of number sequences in quaternion algebra and to contribute to the development of new mathematical tools. Several basic properties of this quaternion family are established, including recurrence relations and Binet-type formulas that provide explicit representations of the terms. Moreover, generating functions and exponential generating functions are derived, offering compact forms and useful analytical frameworks. In addition, a number of fundamental identities are presented to illustrate the structural features of the quaternions under consideration. Finally, the results obtained here not only generalize well-known concepts but also suggest possible applications of higher order Lichtenberg quaternions in combinatorics, coding theory, and theoretical physics.

Keywords

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Gamaliel Morales ^*
0000-0003-3164-4434
Chile

Publication Date

June 30, 2026

Submission Date

October 3, 2025

Acceptance Date

January 9, 2026

Published in Issue

Year 2026 Volume: 18 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1796085

IZ

https://izlik.org/JA87MN58YP

Cite

RIS / Bibtex

APA

Morales, G. (2026). On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components. Turkish Journal of Mathematics and Computer Science, 18(2), 396-405. https://doi.org/10.47000/tjmcs.1796085

AMA

1.Morales G. On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components. TJMCS. 2026;18(2):396-405. doi:10.47000/tjmcs.1796085

Chicago

Morales, Gamaliel. 2026. “On 3-Parameter Generalized Quaternions With Higher Order Lichtenberg Numbers Components”. Turkish Journal of Mathematics and Computer Science 18 (2): 396-405. https://doi.org/10.47000/tjmcs.1796085.

EndNote

Morales G (June 1, 2026) On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components. Turkish Journal of Mathematics and Computer Science 18 2 396–405.

IEEE

[1]G. Morales, “On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components”, TJMCS, vol. 18, no. 2, pp. 396–405, June 2026, doi: 10.47000/tjmcs.1796085.

ISNAD

Morales, Gamaliel. “On 3-Parameter Generalized Quaternions With Higher Order Lichtenberg Numbers Components”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 396-405. https://doi.org/10.47000/tjmcs.1796085.

JAMA

1.Morales G. On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components. TJMCS. 2026;18:396–405.

MLA

Morales, Gamaliel. “On 3-Parameter Generalized Quaternions With Higher Order Lichtenberg Numbers Components”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 396-05, doi:10.47000/tjmcs.1796085.

Vancouver

1.Gamaliel Morales. On 3-parameter Generalized Quaternions with Higher Order Lichtenberg Numbers Components. TJMCS. 2026 Jun. 1;18(2):396-405. doi:10.47000/tjmcs.1796085