TY - JOUR ID - 461 TI - Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Kaygisiz, K. AU - Sahin, A. AD - Gaziosmanpasa University Faculty of Science and Art Department of Mathematics AD - Gaziosmanpasa University Y1 - 2013 PY - 2013 VL - 39 IS - 6 SP - 1065 EP - 1078 KW - Generalized Lucas polynomials KW - generalized Perrin polynomials KW - Hessenberg matrix KW - determinant KW - permanent DO - N2 - 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. UR - http://bims.iranjournals.ir/article_461.html L1 - http://bims.iranjournals.ir/article_461_614511c7f595e147b7d12b7d884a46e1.pdf ER -