Rocky Mountain Journal of Mathematics

Determinantal and permanental representations of Fibonacci type numbers and polynomials

Kenan Kaygisiz and Adem Şahin

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Abstract

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.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 1 (2016), 227-242.

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1464035860

Digital Object Identifier
doi:10.1216/RMJ-2016-46-1-227

Mathematical Reviews number (MathSciNet)
MR3506086

Zentralblatt MATH identifier
06587828

Subjects
Primary: 11B37: Recurrences {For applications to special functions, see 33-XX}
Secondary: 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14] 15A51

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

Citation

Kaygisiz, Kenan; Şahin, Adem. Determinantal and permanental representations of Fibonacci type numbers and polynomials. Rocky Mountain J. Math. 46 (2016), no. 1, 227--242. doi:10.1216/RMJ-2016-46-1-227. https://projecteuclid.org/euclid.rmjm/1464035860


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