Research on the Spinors of Jacobsthal and Jacobsthal–Lucas Hybrid Number Polynomials

Yong Deng and Yanni Yang ()
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Yong Deng: School of Mathematics and Statistics, Xinquan Campus, Kashi University, Xuefu Avenue, Kashi 844000, China
Yanni Yang: School of Mathematics and Statistics, Xinquan Campus, Kashi University, Xuefu Avenue, Kashi 844000, China

Mathematics, 2025, vol. 13, issue 21, 1-12

Abstract: By drawing on the concepts of Jacobsthal polynomials, Jacobsthal–Lucas polynomials, and hybrid numbers, this paper constructs, for the first time, a novel class of mathematical objects with recursive properties—namely, the sequences of Jacobsthal and Jacobsthal–Lucas hybrid number polynomials. Meanwhile, within this framework, this paper further defines their hybrid spinor sequences and explores their core algebraic structures and properties, including Binet-like formulas, generating functions, and the Vajda identity. Finally, the matrix representations of the spinors corresponding to Jacobsthal and Jacobsthal–Lucas hybrid number polynomials are presented.

Keywords: hybrid number; Jacobsthal hybrid polynomial; Jacobsthal–Lucas hybrid number polynomial; hybrid spinor; matrix representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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