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Volume 16
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10.3390/sym16101397
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Article

A New Hybrid Generalization of Balancing Polynomials

by
Dorota Bród
,
Mariola Rubajczyk
* and
Anetta Szynal-Liana
The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2024, 16(10), 1397; https://doi.org/10.3390/sym16101397
Submission received: 27 August 2024 / Revised: 10 October 2024 / Accepted: 16 October 2024 / Published: 21 October 2024
(This article belongs to the Section B: Mathematics)
Versions Notes

Abstract

In this paper, we introduce and study balancing hybrinomials, i.e., polynomials being a generalization of balancing hybrid numbers. We provide some properties of the balancing hybrinomials, including Catalan, Cassini, d’Ocagne, and Vajda identities, among others. Moreover, we present a matrix representation of the hybrinomials.
Keywords: balancing numbers; complex numbers; hyperbolic numbers; dual numbers; polynomials; Diophantine equations balancing numbers; complex numbers; hyperbolic numbers; dual numbers; polynomials; Diophantine equations

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MDPI and ACS Style

Bród, D.; Rubajczyk, M.; Szynal-Liana, A. A New Hybrid Generalization of Balancing Polynomials. Symmetry 2024, 16, 1397. https://doi.org/10.3390/sym16101397

AMA Style

Bród D, Rubajczyk M, Szynal-Liana A. A New Hybrid Generalization of Balancing Polynomials. Symmetry. 2024; 16(10):1397. https://doi.org/10.3390/sym16101397

Chicago/Turabian Style

Bród, Dorota, Mariola Rubajczyk, and Anetta Szynal-Liana. 2024. "A New Hybrid Generalization of Balancing Polynomials" Symmetry 16, no. 10: 1397. https://doi.org/10.3390/sym16101397

APA Style

Bród, D., Rubajczyk, M., & Szynal-Liana, A. (2024). A New Hybrid Generalization of Balancing Polynomials. Symmetry, 16(10), 1397. https://doi.org/10.3390/sym16101397

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