%0 Journal Article
%T Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Kaygisiz, K.
%A Sahin, A.
%D 2013
%\ 12/15/2013
%V 39
%N 6
%P 1065-1078
%! Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
%K Generalized Lucas polynomials
%K generalized Perrin polynomials
%K Hessenberg matrix
%K determinant
%K permanent
%R
%X 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.
%U http://bims.iranjournals.ir/article_461_614511c7f595e147b7d12b7d884a46e1.pdf