FIBONACCI AND LUCAS SEQUENCES AS THE PRINCIPAL MINORS OF SOME INFINITE MATRICES

被引：4

作者：

Moghaddamfar, A. R. ^{[1
]}

Pooya, S. M. H. ^{[1
]}

Salehy, S. Navid ^{[1
]}

Salehy, S. Nima ^{[1
]}

机构：

[1] KN Toosi Univ Technol, Fac Sci, Dept Math, Tehran, Iran

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2009年 / 8卷 / 06期

关键词：

Fibonacci and Lucas k-numbers; determinant; recursive relation; matrix factorization; generalized Pascal triangle; DETERMINANTS;

D O I：

10.1142/S0219498809003734

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the literature one may encounter certain infinite tridiagonal matrices, the principal minors of which, constitute the Fibonacci or Lucas sequence. The major purpose of this article is to find new infinite matrices with this property. It is interesting to mention that the matrices found are not tridiagonal which have been investigated before. Furthermore, we introduce the sequences composed of Fibonacci and Lucas k-numbers for the positive integer k and we construct the infinite matrices the principal minors of which generate these sequences.

引用

页码：869 / 883

页数：15

共 9 条

[1]

Bacher R., 2002, J THEOR NOMBR BORDX, V14, P19

[2]

Cahill N.D., 2002, College Math. J., V33, P221, DOI [DOI 10.1080/07468342.2002.11921945, 10.2307/1559033, DOI 10.2307/1559033]

[3]

Cahill ND, 2004, FIBONACCI QUART, V42, P216

[4] Advanced determinant calculus: A complement [J].

Krattenthaler, C .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 411 :68-166

[5]

Krattenthaler Christian, 1999, Seminaire Lotharingien Combinatoire, V42, pB42q

[6]

Moghaddamfar AR, 2007, ELECTRON J LINEAR AL, V16, P19

[7]

Stakhov A. P., 1977, Introduction into Algorithmic Measurement Theory

[8]

Vajda S, 1989, FIBONACCI LUCAS NUMB

[9] Pascal-like determinants are recursive [J].

Zakrajsek, H ;

Petkovsek, M .

ADVANCES IN APPLIED MATHEMATICS, 2004, 33 (03) :431-450

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