Distance Fibonacci Polynomials by Graph Methods

In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle...

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Autores principales:	Dominik Strzałka, Sławomir Wolski, Andrzej Włoch
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Fibonacci numbers Fibonacci polynomials matrix generators Pascal’s triangle Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/92ae760c477e48868d1b2c7d1cfae792
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spelling	oai:doaj.org-article:92ae760c477e48868d1b2c7d1cfae7922021-11-25T19:06:32ZDistance Fibonacci Polynomials by Graph Methods10.3390/sym131120752073-8994https://doaj.org/article/92ae760c477e48868d1b2c7d1cfae7922021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2075https://doaj.org/toc/2073-8994In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions.Dominik StrzałkaSławomir WolskiAndrzej WłochMDPI AGarticleFibonacci numbersFibonacci polynomialsmatrix generatorsPascal’s triangleMathematicsQA1-939ENSymmetry, Vol 13, Iss 2075, p 2075 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Fibonacci numbers Fibonacci polynomials matrix generators Pascal’s triangle Mathematics QA1-939
spellingShingle	Fibonacci numbers Fibonacci polynomials matrix generators Pascal’s triangle Mathematics QA1-939 Dominik Strzałka Sławomir Wolski Andrzej Włoch Distance Fibonacci Polynomials by Graph Methods
description	In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions.
format	article
author	Dominik Strzałka Sławomir Wolski Andrzej Włoch
author_facet	Dominik Strzałka Sławomir Wolski Andrzej Włoch
author_sort	Dominik Strzałka
title	Distance Fibonacci Polynomials by Graph Methods
title_short	Distance Fibonacci Polynomials by Graph Methods
title_full	Distance Fibonacci Polynomials by Graph Methods
title_fullStr	Distance Fibonacci Polynomials by Graph Methods
title_full_unstemmed	Distance Fibonacci Polynomials by Graph Methods
title_sort	distance fibonacci polynomials by graph methods
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/92ae760c477e48868d1b2c7d1cfae792
work_keys_str_mv	AT dominikstrzałka distancefibonaccipolynomialsbygraphmethods AT sławomirwolski distancefibonaccipolynomialsbygraphmethods AT andrzejwłoch distancefibonaccipolynomialsbygraphmethods
_version_	1718410291400671232

Distance Fibonacci Polynomials by Graph Methods

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