The Padovan-circulant-Hurwitz sequences

Zafer Adigüzel, Özgür Erdağ, Ömür Deveci

Abstract


In this paper, we define the Padovan-circulant-Hurwitz sequences of the first, second, third and fourth kinds by using the Hurwitz matrices, which are obtained from the characteristic polynomials of the Padovan-circulant sequences of the first, second, third and fourth kinds. First, we derive relationships between the Padovan-circulant-Hurwitz numbers of the first, second, third and fourth kinds and the generating matrices of these
sequences. Then we obtain the miscellaneous properties of these sequences by aid of these matrices.


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References


Y. Aküzüm, Ö. Deveci, G. Artun, The adjacency-pell-circulant sequences, Utilitas Mathematica 110 (2019), 49-61.

R.A. Brualdi, P.M. Gibson, Convex polyhedra of doubly stochastic matrices. I. Applications of the permanent function, Journal of Combinatorial Theory, Series A 22 (1977), no. 2, 194-230.

W.Y. Chen, J.D. Louck, The combinatorial power of the companion matrix, Linear Algebra and its Applications 232 (1996), 261-278.

V.W. de Spinadel, The family of metallic means, Visual Mathematics 1 (1999), no. 3, 1-16.

Ö. Deveci, The Padovan-circulant sequences and their applications, Mathematical Reports 20 (2018), no. 70, 401-416.

Ö. Deveci, Y. Aküzüm, The adjacency-Jacobsthal-Hurwitz type numbers, Filomat 32 (2018), no. 16, 5623-5632.

Ö. Deveci, Z. Adıgüzel, Y. Aküzüm, On the Jacobsthal-circulant-Hurwitz numbers, Maejo International Journal of Science & Technology 14 (2020), no. 1, 56-67.

Ö. Deveci, A.G. Shannon, Pell-Padovan{circulant sequences and their applications, Notes on Number Theory and Discrete Mathematics 23 (2017), no. 3, 100-114.

M.S. El Naschie, Deriving the essential features of the standard model from the general theory of relativity, Chaos, Solitons & Fractals 24 (2005), no. 4, 941-946.

J. Hiller, Y. Aküzüm, Ö. Deveci, The Adjacency-Pell-Hurwitz Numbers, Integers 18 (2018), A83.

A. Hurwitz, Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negative reellen Theilen besitzt, Mathematische Annalen 46 (1895), no. 2, 273-284.

D. Kalman, Generalized Fibonacci numbers by matrix methods, Fibonacci Quarterly 20 (1982), no. 1, 73-76.

G.R. Kaluge, Penggunaan Fibonacci dan Josephus problem dalam algoritma enkripsi transposisi+ substitusi, Makalah IF 3058 Kriptogra_-Sem. II Tahun.

E. Kilic, A. Stakhov, On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices, Chaos, Solitons & Fractals 40 (2009), no. 5, 2210-2221.

B. K. Kirchoff, R. Rutishauser, The phyllotaxy of costus (Costaceae), Botanical Gazette 151 (1990), no. 1, 88-105.

F. Kraus, M. Mansour, M. Sebek, Hurwitz matrix for polynomial matrices, In: (R. Jeltsch, M. Mansour (Eds)) Stability Theory: Hurwitz Centenary Conference Centro Stefano Franscini, Ascona, Switzerland, 1995, Birkhäuser, 2012, 67-74.

P. Lancaster, M. Tismenetsky, The theory of matrices: with applications, Elsevier, 1985.

R. Lidl, H. Niederreiter, Introduction to _nite _elds and their applications, Cambridge University Press, 1994.

L. Lipshitz, A. van der Poorten, Rational functions, diagonals, automata and arithm, In: (R. Mollin (Ed.)) Number Theory: Proceedings of the First Conference of the Canadian Number Theory Association held at the Banff Center, Banff, Alberta, April 17{27, 1988, de Grutyer, Berlin, 1990, 339-358.

D. Mandelbaum, Synchronization of codes by means of Kautz's Fibonacci encoding, IEEE Transactions on Information Theory 18 (1972), no. 2, 281-285.

Y. Matiyasevich, Hilbert's tenth problem, MIT Press, 1993.

A.G. Shannon, L. Bernstein, The Jacobi-Perron algorithm and the algebra of recursive sequences, Bulletin of the Australian Mathematical Society 8 (1973), no. 2, 261-277.

W. Stein, Modeling the evolution of stelar architecture in vascular plants, International Journal of Plant Sciences 154 (1993), no. 2, 229-263.

I. Stewart, Mathematical recreations, Scientific American 275 (1996), no. 2, 100-103.

R. Stroeker, Brocard Points, Circulant Matrices, and Descartes' Folium, Mathematics Magazine 61 (1988), no. 3, 172-187.




DOI: https://doi.org/10.52846/ami.v52i2.1947