On the Permanents of Some Tridiagonal Matrices with Applications to the Fibonacci and Lucas Numbers

Kılıç, Emrah; Tasci, Dursun

doi:10.1216/rmjm/1199649832

Cited by 24 publications

(16 citation statements)

References 5 publications

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“…Number theoretic properties such as these obtained from Fibonacci numbers relevant to this paper have been studied by many authors [1,4,7,11,12,20,23,27,28]. Now we define the generalized Fibonacci-circulant-Hurwitz numbers and then, we obtain their miscellaneous properties using the generating matrix and the generating function of these numbers.…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Fibonacci-circulant-Hurwitz numbers

Devecı¹,

Adıgüzel²,

Doğan³

2020

NNTDM

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The theory of Fibonacci-circulant numbers was introduced by Deveci et al. (see [5]). In this paper, we define the Fibonacci-circulant-Hurwitz sequence of the second kind by Hurwitz matrix of the generating function of the Fibonacci-circulant sequence of the second kind and give a fair generalization of the sequence defined, which we call the generalized Fibonacci-circulant-Hurwitz sequence. First, we derive relationships between the generalized Fibonacci-circulant-Hurwitz numbers and the generating matrices for these numbers. Also, we give miscellaneous properties of the generalized Fibonacci-circulant-Hurwitz numbers such as the Binet formula, the combinatorial, permanental, determinantal representations, the generating function, the exponential representation and the sums.

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Section: Introductionmentioning

confidence: 99%

On the Generalized Fibonacci-circulant-Hurwitz numbers

Devecı¹,

Adıgüzel²,

Doğan³

2020

NNTDM

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“…Lehmer [7] demonstrated some generalizations for the permanent of a tridiagonal matrix by using expansion by minors. Kılıc and Tascı [8] presented some relationships between the permanents of some tridiagonal matrices and some famous number sequences. Jina and Trojovsky [9] presented new results about the relationships between the permanents of some tridiagonal matrices and the Fibonacci numbers.…”

Section: Introductionmentioning

confidence: 99%

Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz matrix and the Chebyshev polynomials

Küçük¹,

Düz²

2017

J. Appl. Math. Comput. Mech.

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“…In [11], the authors presented a nice result involving the permanent of an (−1, 0, 1)−matrix and the Fibonacci number F n+1 . The authors then explored similar directions involving the positive subscripted Fibonacci and Lucas Numbers as well as their uncommon negatively subscripted counterparts.…”

Section: Introductionmentioning

confidence: 99%