Determinant Representations of Sequences: A Survey-Reference-Cited by-同舟云学术

Determinant Representations of Sequences: A Survey

Published:2014-01-01 Issue:1 Volume:2 Page:
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Moghaddamfar A. R.¹,Salehy S. Navid²,Salehy S. Nima²

Affiliation:

1. Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran

2. Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA

Abstract

Abstract This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or nonhomogeneous recurrence relations, and others are constructed by convolution of two sequences. In this article, we will illustrate the idea of these methods by constructing some integer matrices of this type.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.2478/spma-2014-0005/pdf

Reference20 articles.

1. [1] R. Bacher, Determinants of matrices related to the Pascal triangle, J. Théor. Nombres Bordeaux, 14(1)(2002), 19-41.

2. [2] P. F. Byrd, Problem B-12: A Lucas determinant, Fibonacci Quart., 1(4)(1963), 78.

3. [3] N. D. Cahill, J. R. D’Errico, D. A. Narayan and J. Y. Narayan, Fibonacci determinants, College Math. J., 33(3)(2002), 221-225.10.2307/1559033

4. [4] N. D. Cahill, J. R. D’Errico and J. P. Spence, Complex factorizations of the Fibonacci and Lucas numbers, Fibonacci Quart., 41(1)(2003), 13-19.

5. [5] N. D. Cahill and D. A. Narayan, Fibonacci and Lucas numbers as tridiagonal matrix determinants, Fibonacci Quart., 42(3)(2004), 216-221.

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