İki değişkenli Balans ve Lucas-Balans polinomlarının üreteç matrisleri

Year 2021, Volume: 11 Issue: 3, 761 - 767, 15.07.2021

Nazmiye Yılmaz

https://doi.org/10.17714/gumusfenbil.841087

Abstract

Makalenin amacı iki değişkenli Balans ve Lucas-Balans polinomlarını üçgensel matrislerin determinantları ile ifade etmektir. Ek olarak bu üçgensel matrislerin terslerini elde ettik. Determinantları iki değişkenli Balans ve Lucas-Balans polinomlarının herhangi pozitif ve negatif indisli lineer alt dizilerini üreten üçgensel matrislerin ailesini veren genel sonuçlar ile sonlandırdık.

Keywords

Balans polinomları, Determinant, Matris tersi, Lucas-balans polinomları, Üçgensel matris

The generating matrices of the bivariate Balancing and Lucas-Balancing polynomials

Abstract

The objective of this paper is to express the bivariate Balancing and Lucas-Balancing polynomials in terms of determinants of tridiagonal matrices. In addition, we obtained the inverses of the tridiagonal matrices. We finalized the general results to construct families of the tridiagonal matrices whose determinants generate arbitrary linear subsequence with positive and negative indices of the bivariate Balancing and Lucas-Balancing polynomials.

Keywords

Balancing polynomials, Determinant, Inverse of matrix, Lucas-Balancing polynomials, Tridiagonal matrix

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