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

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Języki publikacji
EN
Abstrakty
EN
In this study, the recursive relations between the permanents of a certain type of the k-tridiagonal symmetric Toeplitz matrix with complex entries and the Chebyshev polynomials of the second kind are presented.
Rocznik
Strony
75--86
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
  • Eskipazar Vocational School Turkey
autor
  • Department of Mathematics Faculty of Science, Karabuk University Turkey
Bibliografia
  • [1] Mazilu I., Mazilu D.A., Williams H.T., Applications of tridiagonal matrices in non-equilibrium statistical physics, Electronic Journal of Linear Algebra 2012, 24, 7-17.
  • [2] Fontanelli D., Palopoli L., Passerone R., On the Global Convergence of a Class of Distributed Algorithms for Maximizing the Coverage of a WSN, 28th Chinese Control Conference, Shanghai 2009 (IEEE, 2009), pp. 7885 - 7890.
  • [3] Martínez S., Bullo F., Cortés J., Frazzoli E., On synchronous robotic networks - Part I: Models, tasks, and complexity, IEEE Transactions On Automatic Control 2007, 52(12).
  • [4] Poker G., Margaliot M., Tuller T., Sensitivity of mRNA translation, Scientific Reports 5, Article number: 12795, (2015).
  • [5] Brualdi R.A., Gibson P.M., Convex polyhedra of doubly stochastic matrices. I: Applications of the permanent function, The Journal of Combinatorial Theory A 1977, 22, 194-230.
  • [6] Minc H., On permanents of circulants, Pacific Journal of Mathematics 1972, 42(2).
  • [7] Lehmer D., Fibonacci and related sequences in periodic tridiagonal matrices, Fib. Quart. 1975, 13, 150-158.
  • [8] Kilic E., Tasci D., On the permanents of some tridiagonal matrices with applications to the Fibonacci and Lucas numbers, Rocky Mountain J. Math. 2007, 37(6), 1953-1969.
  • [9] Jina J., Trojovsky P., On permanents of some tridiagonal matrices connected with Fibonacci numbers, International Journal of Pure and Applied Mathematics 2014, 97(1), 79-87.
  • [10] Matousova I., Trojovsky P., On a sequence of tridiagonal matrices, whose permanents are related to Fibonacci and Lucas numbers, International Journal of Pure and Applied Mathematics 2015, 105(4), 715-723.
  • [11] Kaygısız K., Sahin A., Determinant and permanent of Hessenberg matrix and Fibonacci type Numbers, Gen. Math. Notes 2012, 9(2), 32-41.
  • [12] Kırklar E., Yılmaz F., A note on k-tridiagonal k-Toeplitz matrices, Alabama Journal of Mathematics 2015, 39.
  • [13] Yılmaz F., Bozkurt D., The adjacency matrix of one type of directed graph and the Jacobsthal numbers and their determinantal representation, Journal of Applied Mathematics 2012.
  • [14] Elouafi M., On a relationship between Chebyshev polynomials and Toeplitz determinants, Applied Mathematics and Computation 2014, 229, 27-33.
  • [15] Cahill N.D., Derrico J.R., Spence J.P., Complex factorizations of the Fibonacci and Lucas numbers, Fibonacci Quarterly 2003, 41(1), 13-19.
  • [16] Kılıç E., On a constant-diagonals matrix, Applied Mathematics and Computation 2008, 204(1), 184-190.
  • [17] Asci M., Tasci D., El-Mikkawy M., On determinants and permanents of k-tridiagonal Toeplitz matrices, Util. Math. 2012, 89, 97-106.
  • [18] Trench W.F., Banded Symmetric Toeplitz Matrices (Lecture of Mathematic Seminar, Trinity University, 2009).
  • [19] Bergun G.E., Hoggatt V.E., A family of tridiagonal matrices, Fibonacci Quart. 1978, 16, 285-288.
  • [20] Mason J.C., Handscomb D.C., Chebyshev Polynomials, Chapman Hall/CRC, Boca Raton 2003.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7987a3fd-474a-470d-ac87-599a61188d74
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