Determinant Representations of Sequences: A Survey

A. R. Moghaddamfar; S. Navid Salehy; S. Nima Salehy

Special Matrices (2014)

  • Volume: 2, Issue: 1, page 46-60
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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A. R. Moghaddamfar, S. Navid Salehy, and S. Nima Salehy. "Determinant Representations of Sequences: A Survey." Special Matrices 2.1 (2014): 46-60. <http://eudml.org/doc/267229>.

@article{A2014,
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.},
author = {A. R. Moghaddamfar, S. Navid Salehy, S. Nima Salehy},
journal = {Special Matrices},
keywords = {determinant; generalized Pascal triangle; (Quasi) Toeplitz matrix; (Quasi) Pascal-like matrix; Fibonacci (Lucas; Jacobsthal and Pell) sequence; (quasi) Toeplitz matrix; (quasi) Pascal-like matrix; Fibonacci (Lucas, Jacobsthal and Pell) sequence},
language = {eng},
number = {1},
pages = {46-60},
title = {Determinant Representations of Sequences: A Survey},
url = {http://eudml.org/doc/267229},
volume = {2},
year = {2014},
}

TY - JOUR
AU - A. R. Moghaddamfar
AU - S. Navid Salehy
AU - S. Nima Salehy
TI - Determinant Representations of Sequences: A Survey
JO - Special Matrices
PY - 2014
VL - 2
IS - 1
SP - 46
EP - 60
AB - 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.
LA - eng
KW - determinant; generalized Pascal triangle; (Quasi) Toeplitz matrix; (Quasi) Pascal-like matrix; Fibonacci (Lucas; Jacobsthal and Pell) sequence; (quasi) Toeplitz matrix; (quasi) Pascal-like matrix; Fibonacci (Lucas, Jacobsthal and Pell) sequence
UR - http://eudml.org/doc/267229
ER -

References

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