Journal of Integer Sequences, Vol. 15 (2012), Article 12.3.4

Generalized Bivariate Lucas p-Polynomials and Hessenberg Matrices


Kenan Kaygisiz and Adem Şahin
Department of Mathematics
Faculty of Arts and Sciences
Gaziosmanpaşa University
60250 Tokat
Turkey

Abstract:

In this paper, we give some determinantal and permanental representations of generalized bivariate Lucas p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate Lucas p-polynomials are general forms of, for example, bivariate Jacobsthal-Lucas, bivariate Pell-Lucas p-polynomials, Chebyshev polynomials of the first kind, Jacobsthal-Lucas numbers etc.


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Received November 30 2011; revised version received February 21 2012. Published in Journal of Integer Sequences, March 11 2012.


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