Open Access
Translator Disclaimer
2016 Determinantal and permanental representations of Fibonacci type numbers and polynomials
Kenan Kaygisiz, Adem Şahin
Rocky Mountain J. Math. 46(1): 227-242 (2016). DOI: 10.1216/RMJ-2016-46-1-227


In this paper, we compute terms of the matrix $A_{(k)}^{\infty }$, which contains Fibonacci type numbers and polynomials, with the help of determinants and permanents of various Hessenberg matrices. In addition, we show that determinants of these Hessenberg matrices can be obtained by using combinations. The results that we obtain are important, since the matrix $A_{(k)}^{\infty } $ is a general form of Fibonacci type numbers and polynomials, such as $k$ sequences of the generalized order-$k$ Fibonacci and Pell numbers, generalized bivariate Fibonacci $p$-polynomials, bivariate Fibonacci and Pell $p$-polynomials, second kind Chebyshev polynomials and bivariate Jacobsthal polynomials, etc.


Download Citation

Kenan Kaygisiz. Adem Şahin. "Determinantal and permanental representations of Fibonacci type numbers and polynomials." Rocky Mountain J. Math. 46 (1) 227 - 242, 2016.


Published: 2016
First available in Project Euclid: 23 May 2016

zbMATH: 06587828
MathSciNet: MR3506086
Digital Object Identifier: 10.1216/RMJ-2016-46-1-227

Primary: 11B37
Secondary: 15A15 , 15A51

Keywords: generalized Fibonacci polynomials , Hessenberg matrix , Matrix $A_(k)^\infty $

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium


Vol.46 • No. 1 • 2016
Back to Top