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BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 11, 65 - 71, 30.12.2019

Öz

Kaynakça

  • Brualdi, R., Gibson, P., {\em Convex polyhedra of doubly stochastic matrices. I. Applications of the permanent function}, J. Comb. Theory, \textbf{22(2)}(1977), 194--230.
  • Cahill, N.D., D'Errico, J.R., Narayan, D.A., Narayan, J.Y., {\em Fibonacci determinants}, College Math. J., \textbf{33(3)}(2002), 221--225.
  • H.H., {\em Permanents and determinants of tridiagonal matrices with (s, t)-Pell Lucas numbers}, International Journal of Mathematical Analysis, \textbf{11(23)}(2017), 1117--1122.
  • Kayg\i s\i z, K., Sahin, A., {\em Determinant and permanent of Hessenberg matrices and Fibonacci type numbers}, Gen. Math. Notes, \textbf{9(2)}(2012), 32--41.
  • K\i l\i c, E., Ta\c{s}\c{c}\i , D., {\em On the permanents of some tridiagonal matrices with applicationsto the Fibonacci and Lucas numbers}, Rocky Mt. J. Math., \textbf{37}(2007), 1953--1969.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
  • Koshy, T., {\em Fibonacci, Lucas and Pell numbers, and Pascal's triangle}, Math. Spectrum, \textbf{43}(2011), 125--132.
  • Lee, G.Y., {\em $k$-Lucas numbers and associated bipartite graphs}, Linear Algebra Appl., \textbf{320}(2000), 51--61.
  • Minc, H., Permanents, Encyclopedia Math. Appl., 6, London: Addison-Wesley Publishing Company, 1978.
  • Morteza, E., {\em More on the Fibonacci sequence and Hessenberg matrices}, Integers, \textbf{6}(2006), A32.
  • Ocal, A.A., Tuglu, N., Altinisik, E., {\em On the representation of k-generalized Fibonacci and Lucas numbers}, Appl. Math. Comput., \textbf{170(1)}(2005), 584--596.
  • Serre, D., Matrices: Theory and Applications, New York: Springer Verlag, 2002.
  • Singh, B., Sikhwal O., Bhatnagar, S., {\em Fibonacci-like sequence and its properties}, Int. J. Contemp. Math. Sciences, \textbf{5(18)}(2010), 859--868.
  • Strang, G., Introduction to Linear Algebra, 2nd Ed., Wellesley MA, Wellesley-Cambridge, 1998.
  • Ta\c{s}yurdu, Y., {\em On generalized Fibonacci-like sequences by Hessenberg matrices}, International Journal of Mathematics Trends and Technology, \textbf{64(1)}(2018), 51-58.
  • Ta\c{s}yurdu, Y., \c{C}obanoglu N., Dilmen Z., {\em On the a new family of $k$-Fibonacci numbers}, Erzincan University Journal of Science and Technology, \textbf{9(1)}(2016), 95--101.
  • Ta\c{s}yurdu, Y., G\"{u}ltekin I, {\em Determinantal and permanental representation of $q$-Fibonacci polynomials}, Qscience Connect, \textbf{25}(2014), 5p.
  • Wani, A.A., Sikhwal, O.P., Sisodiya, K., {\em Relations among Fibonacci, Lucas and Fibonacci-like sequences}, International Journal of Recent Trends in Engineering \& Research, \textbf{2(9)}(2016), 125--136.
  • Y\i lmaz, F., Bozkurt, D., {\em Hessenberg matrices and the Pell and Perrin numbers}, J. Number Theory., \textbf{131}(2011), 1390--1396.

Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences

Yıl 2019, Cilt: 11, 65 - 71, 30.12.2019

Öz

In this paper, we consider Hessenberg matrices and Fibonacci-Like sequences that is defined by the recurrence relation $T_{n}=T_{n-1}+T_{n-2}$, $% n\geq 2$ and $T_{0}=m$, $T_{1}=m$ where $m$ is a fixed positive integer. We define two $n\times n$ Hessenberg matrices with applications to the Fibonacci-Like sequences and investigate the determinantal and permanental properties. We obtain that the determinants and permanents of these Hessenberg matrices are equal to the $n$th term of Fibonacci-Like sequences.

Kaynakça

  • Brualdi, R., Gibson, P., {\em Convex polyhedra of doubly stochastic matrices. I. Applications of the permanent function}, J. Comb. Theory, \textbf{22(2)}(1977), 194--230.
  • Cahill, N.D., D'Errico, J.R., Narayan, D.A., Narayan, J.Y., {\em Fibonacci determinants}, College Math. J., \textbf{33(3)}(2002), 221--225.
  • H.H., {\em Permanents and determinants of tridiagonal matrices with (s, t)-Pell Lucas numbers}, International Journal of Mathematical Analysis, \textbf{11(23)}(2017), 1117--1122.
  • Kayg\i s\i z, K., Sahin, A., {\em Determinant and permanent of Hessenberg matrices and Fibonacci type numbers}, Gen. Math. Notes, \textbf{9(2)}(2012), 32--41.
  • K\i l\i c, E., Ta\c{s}\c{c}\i , D., {\em On the permanents of some tridiagonal matrices with applicationsto the Fibonacci and Lucas numbers}, Rocky Mt. J. Math., \textbf{37}(2007), 1953--1969.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
  • Koshy, T., {\em Fibonacci, Lucas and Pell numbers, and Pascal's triangle}, Math. Spectrum, \textbf{43}(2011), 125--132.
  • Lee, G.Y., {\em $k$-Lucas numbers and associated bipartite graphs}, Linear Algebra Appl., \textbf{320}(2000), 51--61.
  • Minc, H., Permanents, Encyclopedia Math. Appl., 6, London: Addison-Wesley Publishing Company, 1978.
  • Morteza, E., {\em More on the Fibonacci sequence and Hessenberg matrices}, Integers, \textbf{6}(2006), A32.
  • Ocal, A.A., Tuglu, N., Altinisik, E., {\em On the representation of k-generalized Fibonacci and Lucas numbers}, Appl. Math. Comput., \textbf{170(1)}(2005), 584--596.
  • Serre, D., Matrices: Theory and Applications, New York: Springer Verlag, 2002.
  • Singh, B., Sikhwal O., Bhatnagar, S., {\em Fibonacci-like sequence and its properties}, Int. J. Contemp. Math. Sciences, \textbf{5(18)}(2010), 859--868.
  • Strang, G., Introduction to Linear Algebra, 2nd Ed., Wellesley MA, Wellesley-Cambridge, 1998.
  • Ta\c{s}yurdu, Y., {\em On generalized Fibonacci-like sequences by Hessenberg matrices}, International Journal of Mathematics Trends and Technology, \textbf{64(1)}(2018), 51-58.
  • Ta\c{s}yurdu, Y., \c{C}obanoglu N., Dilmen Z., {\em On the a new family of $k$-Fibonacci numbers}, Erzincan University Journal of Science and Technology, \textbf{9(1)}(2016), 95--101.
  • Ta\c{s}yurdu, Y., G\"{u}ltekin I, {\em Determinantal and permanental representation of $q$-Fibonacci polynomials}, Qscience Connect, \textbf{25}(2014), 5p.
  • Wani, A.A., Sikhwal, O.P., Sisodiya, K., {\em Relations among Fibonacci, Lucas and Fibonacci-like sequences}, International Journal of Recent Trends in Engineering \& Research, \textbf{2(9)}(2016), 125--136.
  • Y\i lmaz, F., Bozkurt, D., {\em Hessenberg matrices and the Pell and Perrin numbers}, J. Number Theory., \textbf{131}(2011), 1390--1396.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Yasemin Taşyurdu 0000-0002-9011-8269

Fikret Işık Bu kişi benim 0000-0003-3823-3312

Yayımlanma Tarihi 30 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 11

Kaynak Göster

APA Taşyurdu, Y., & Işık, F. (2019). Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences. Turkish Journal of Mathematics and Computer Science, 11, 65-71.
AMA Taşyurdu Y, Işık F. Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences. TJMCS. Aralık 2019;11:65-71.
Chicago Taşyurdu, Yasemin, ve Fikret Işık. “Determinants and Permanents of Hessenberg Matrices With Fibonacci-Like Sequences”. Turkish Journal of Mathematics and Computer Science 11, Aralık (Aralık 2019): 65-71.
EndNote Taşyurdu Y, Işık F (01 Aralık 2019) Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences. Turkish Journal of Mathematics and Computer Science 11 65–71.
IEEE Y. Taşyurdu ve F. Işık, “Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences”, TJMCS, c. 11, ss. 65–71, 2019.
ISNAD Taşyurdu, Yasemin - Işık, Fikret. “Determinants and Permanents of Hessenberg Matrices With Fibonacci-Like Sequences”. Turkish Journal of Mathematics and Computer Science 11 (Aralık 2019), 65-71.
JAMA Taşyurdu Y, Işık F. Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences. TJMCS. 2019;11:65–71.
MLA Taşyurdu, Yasemin ve Fikret Işık. “Determinants and Permanents of Hessenberg Matrices With Fibonacci-Like Sequences”. Turkish Journal of Mathematics and Computer Science, c. 11, 2019, ss. 65-71.
Vancouver Taşyurdu Y, Işık F. Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences. TJMCS. 2019;11:65-71.