Spectral properties of a functional binomial matrix

Morteza Bayat

Makale detayları

Spectral properties of a functional binomial matrix

Yazarlar:

Morteza Bayat

Yayıncı:

Ankara University

Ana Başlıklar:

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 3, pp.749-764

Belge Tipi:

Makale

Yayın Tarihi:

9/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001326406

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 In this article, we consider the definition of the Fibonacci polynomial sequence with the second-order linear recurrence relation, where coefficients and initial conditions depend on the variable t. And then, we introduce the functional binomial matrix depending on the coefficients of the second-order linear recurrence relation. In the following, we study the spectral properties of the functional binomial matrix using the Fibonacci polynomial sequence and we obtain a diagonal decomposition for it using the Vandermunde matrix. Finally, by applying some linear algebra tools we obtain a number of combinatorial identities involving the Fibonacci polynomial sequence.

 In this article, we consider the definition of the Fibonacci polynomial sequence with the second-order linear recurrence relation, where coefficients and initial conditions depend on the variable t. And then, we introduce the functional binomial matrix depending on the coefficients of the second-order linear recurrence relation. In the following, we study the spectral properties of the functional binomial matrix using the Fibonacci polynomial sequence and we obtain a diagonal decomposition for it using the Vandermunde matrix. Finally, by applying some linear algebra tools we obtain a number of combinatorial identities involving the Fibonacci polynomial sequence.

 In this article, we consider the definition of the Fibonacci polynomial sequence with the second-order linear recurrence relation, where coefficients and initial conditions depend on the variable t. And then, we introduce the functional binomial matrix depending on the coefficients of the second-order linear recurrence relation. In the following, we study the spectral properties of the functional binomial matrix using the Fibonacci polynomial sequence and we obtain a diagonal decomposition for it using the Vandermunde matrix. Finally, by applying some linear algebra tools we obtain a number of combinatorial identities involving the Fibonacci polynomial sequence.

 In this article, we consider the definition of the Fibonacci polynomial sequence with the second-order linear recurrence relation, where coefficients and initial conditions depend on the variable t. And then, we introduce the functional binomial matrix depending on the coefficients of the second-order linear recurrence relation. In the following, we study the spectral properties of the functional binomial matrix using the Fibonacci polynomial sequence and we obtain a diagonal decomposition for it using the Vandermunde matrix. Finally, by applying some linear algebra tools we obtain a number of combinatorial identities involving the Fibonacci polynomial sequence.

Makale detayları

Spectral properties of a functional binomial matrix

Yazarlar:

Morteza Bayat

Yayıncı:

Ankara University

Ana Başlıklar:

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 3, pp.749-764

Belge Tipi:

Makale

Yayın Tarihi:

9/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001326406

pISSN:

1303-5991

Functional Fibonacci matrix

generalized Fibonacci sequence

generalized Fibonacci polynomial

characteristic polynomial

Pascal matrix

functional binomial matrix

Sayı

Makale detayları

Spectral properties of a functional binomial matrix

Yazarlar: Morteza Bayat

Yayıncı: Ankara University

Ana Başlıklar: Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 3, pp.749-764

Belge Tipi: Makale

Yayın Tarihi: 9/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001326406

pISSN: 1303-5991

Functional Fibonacci matrix

generalized Fibonacci sequence

generalized Fibonacci polynomial

characteristic polynomial

Pascal matrix

functional binomial matrix

Sayı

Yazarlar:

Morteza Bayat

Yayıncı:

Ankara University

Ana Başlıklar:

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 3, pp.749-764

Belge Tipi:

Makale

Yayın Tarihi:

9/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001326406

pISSN:

1303-5991