ARTICLE | doi:10.20944/preprints202008.0272.v1
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Bohemian; Toeplitz matrix; Hessenberg matrix; tridiagonal matrix; pentadiagonal matrix
Online: 12 August 2020 (06:00:31 CEST)
In this paper, we deduce explicit formulas to evaluate the determinants of nonsymmetrical structure Toeplitz Bohemians by two determinants of specific Hessenberg Toeplitz matrices, which are linear combinations in terms of determinants of specific Hessenberg Toeplitz matrices. We get some new results very di¤erent from [Massimiliano Fasi, Gian Maria Negri Porzio, Determinants of normalized upper Hessenberg matrices, Electronic Journal of Linear Algebra, Volume 36, pp. 352-366, June 2020].
ARTICLE | doi:10.20944/preprints201703.0208.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: closed expression; Fibonacci number; Fibonacci polynomial; tridiagonal determinant; Hessenberg determinant
Online: 28 March 2017 (03:11:06 CEST)
In the paper, the authors nd a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.
SHORT NOTE | doi:10.20944/preprints201610.0034.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: determinantal expression; recurrence relation; Euler polynomial; Euler number; Hessenberg determinant
Online: 11 October 2016 (10:40:02 CEST)
In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.
ARTICLE | doi:10.20944/preprints201610.0035.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: derangement number; closed form; Hessenberg determinant; tridiagonal determinant; generating function; recurrence relation; derivative
Online: 11 October 2016 (10:53:07 CEST)
In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.