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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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 39
issue 6 2013
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