Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
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Abstract:
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the conditions under which the determinants of the Hessenberg matrix become its permanents.
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∗Received by the editors January 7, 2008. Accepted for publication on January 13, 2010. Handling Editor: Shmuel Friedland. †Department of Mathematics & Statistics, California State Polytechnic University, Pomona, Pomona, California 91768, USA ([email protected]). ‡Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071, USA ([email protected]). Electronic Journal of Linea...
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Journal title
volume 39 issue 6
pages 1065- 1078
publication date 2013-12-15
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