BibTex RIS Kaynak Göster

On the generalized Perrin and Cordonnier matrices

Yıl 2017, Cilt: 66 Sayı: 1, 242 - 253, 01.02.2017
https://doi.org/10.1501/Commua1_0000000793

Kaynakça

  • Bartlett, C. and Huylebrouck D., Art and math of the 1:35 ratio rectangle, Symmetry: Culture and Science. 24(2013).
  • Brawer, R. and Pirovino M., The linear algebra of the Pascal matrix, Linear Algebra Appl. 174(1992), 13–23.
  • Cahill, N.D., D’Errico J.R., Narayan D.A. and Narayan J.Y., Fibonacci determinants, College Math. J. 33(2002), 221–225.
  • Gibson, P. M., An identity between permanents and determinants, Amer. Math. Monthly. 76(1969), 270–271.
  • Kaygisiz, K., Bozkurt D., k-Generalized Order-k Perrin Number Presentation by Matrix Method, Ars Combinatoria, 105(2012), 95-101.
  • Kaygisiz, K. and Sahin A., Generalized bivariate Lucas p-Polynomials and Hessenberg Ma- trices, J. Integer Seq. 15 Article 12.3.4.(2012).
  • Kaygisiz, K. and Sahin A., Determinant and permanent of Hessenberg matrix and generalized Lucas polynomials, Bull. Iranian Math. Soc. 39(6)(2013), 1065–1078.
  • Kaygisiz, K. and Sahin A., A new method to compute the terms of generalized order-k Fibonacci numbers, J. Number Theory. 133(2013), 3119–3126.
  • Kaygisiz, K. and Sahin A., Generalized Van der Laan and Perrin Polynomials, and Generaliza- tions of Van der Laan and Perrin Numbers, Selçuk Journal of Applied Math., 14(1)(2013),89- 103.
  • Kaygisiz, K. and Sahin A., Calculating terms of associated polynomials of Perrin and Cor- donnier numbers, Notes on Number Theory and Discrete Mathematics, 20(1)(2014),10-18.
  • Kilic, E. and Stakhov A.P., On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices, Chaos Solitons Fractals. 40(2009), 2210–2221.
  • Kilic, E. and Tasci D., The linear algebra of the Pell matrix, Bol. Soc. Mat. Mexicana. 2(11)(2005), 163-174.
  • Lee, G.Y., Kim J.S. and Lee S.G., Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 40(3)(2002), 203–211.
  • Lee, G.Y. and Kim J.S., The linear algebra of the k-Fibonacci matrix, Linear Algebra Appl. 373(2003), 75–87.
  • Li, H-C., On Fibonacci-Hessenberg matrices and the Pell and Perrin numbers, Appl. Math. Comput. 218(17)(2012), 8353–8358.
  • Li, H. and MacHenry T., Permanents and Determinants, Weighted Isobaric Polynomials, and Integer Sequences, Journal of Integer Sequences. 16 (2013)Article 13.3.5
  • Marohni´c, L. and Strmeµcki T., Plastic Number: Construction and Applications, Advanced Research in Scienti…c Areas. (3)7(2012), 1523-1528.
  • Minc, H. Encyclopedia of Mathematics and its Applications, Permanents, Vol.6, Addison- Wesley Publishing Company, 1978.
  • Ocal, A.A., Tuglu N. and Altinisik E., On the representation of k-generalized Fibonacci and Lucas numbers, Appl. Math. Comput. 170(1)(2005), 584–596.
  • Padovan, R., Dom Hans Van Der Laan and the Plastic Number, Nexus IV: Architecture and Mathematics, eds. Kim Williamsand Jose Francisco Rodrigues, Fucecchio (Florence): Kim Williams Books, 2002.
  • Padovan, R., Dom Hans van der Laan: Modern Primitive, Architectura Natura Press, 1994. [22] Shannon, A.G., Anderson P.G. and Horadam A. F., Properties of Cordonnier, Perrin and Van der Laan numbers. International Journal of Mathematical Education in Science and Technology. 37(2006), 825-831.
  • Sahin, A., On the Q analogue of …bonacci and lucas matrices and …bonacci polynomials, Utilitas Mathematica, 100(2016), 113–125.
  • Sahin, A. and Ramírez, J. R., Determinantal and permanental representations of convolved Lucas polynomials, Appl. Math. Comput., 281(2016), 314–322.
  • Yilmaz, F. and Bozkurt D., Hessenberg matrices and the Pell and Perrin numbers, J. Number Theory. 131(8)(2011),1390–1396.
  • Yilmaz, N. and Taskara N., Matrix Sequences in terms of Padovan and Perrin Numbers, Journal of Applied Mathematics (2013), Article ID 941673.
Yıl 2017, Cilt: 66 Sayı: 1, 242 - 253, 01.02.2017
https://doi.org/10.1501/Commua1_0000000793

Kaynakça

  • Bartlett, C. and Huylebrouck D., Art and math of the 1:35 ratio rectangle, Symmetry: Culture and Science. 24(2013).
  • Brawer, R. and Pirovino M., The linear algebra of the Pascal matrix, Linear Algebra Appl. 174(1992), 13–23.
  • Cahill, N.D., D’Errico J.R., Narayan D.A. and Narayan J.Y., Fibonacci determinants, College Math. J. 33(2002), 221–225.
  • Gibson, P. M., An identity between permanents and determinants, Amer. Math. Monthly. 76(1969), 270–271.
  • Kaygisiz, K., Bozkurt D., k-Generalized Order-k Perrin Number Presentation by Matrix Method, Ars Combinatoria, 105(2012), 95-101.
  • Kaygisiz, K. and Sahin A., Generalized bivariate Lucas p-Polynomials and Hessenberg Ma- trices, J. Integer Seq. 15 Article 12.3.4.(2012).
  • Kaygisiz, K. and Sahin A., Determinant and permanent of Hessenberg matrix and generalized Lucas polynomials, Bull. Iranian Math. Soc. 39(6)(2013), 1065–1078.
  • Kaygisiz, K. and Sahin A., A new method to compute the terms of generalized order-k Fibonacci numbers, J. Number Theory. 133(2013), 3119–3126.
  • Kaygisiz, K. and Sahin A., Generalized Van der Laan and Perrin Polynomials, and Generaliza- tions of Van der Laan and Perrin Numbers, Selçuk Journal of Applied Math., 14(1)(2013),89- 103.
  • Kaygisiz, K. and Sahin A., Calculating terms of associated polynomials of Perrin and Cor- donnier numbers, Notes on Number Theory and Discrete Mathematics, 20(1)(2014),10-18.
  • Kilic, E. and Stakhov A.P., On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices, Chaos Solitons Fractals. 40(2009), 2210–2221.
  • Kilic, E. and Tasci D., The linear algebra of the Pell matrix, Bol. Soc. Mat. Mexicana. 2(11)(2005), 163-174.
  • Lee, G.Y., Kim J.S. and Lee S.G., Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 40(3)(2002), 203–211.
  • Lee, G.Y. and Kim J.S., The linear algebra of the k-Fibonacci matrix, Linear Algebra Appl. 373(2003), 75–87.
  • Li, H-C., On Fibonacci-Hessenberg matrices and the Pell and Perrin numbers, Appl. Math. Comput. 218(17)(2012), 8353–8358.
  • Li, H. and MacHenry T., Permanents and Determinants, Weighted Isobaric Polynomials, and Integer Sequences, Journal of Integer Sequences. 16 (2013)Article 13.3.5
  • Marohni´c, L. and Strmeµcki T., Plastic Number: Construction and Applications, Advanced Research in Scienti…c Areas. (3)7(2012), 1523-1528.
  • Minc, H. Encyclopedia of Mathematics and its Applications, Permanents, Vol.6, Addison- Wesley Publishing Company, 1978.
  • Ocal, A.A., Tuglu N. and Altinisik E., On the representation of k-generalized Fibonacci and Lucas numbers, Appl. Math. Comput. 170(1)(2005), 584–596.
  • Padovan, R., Dom Hans Van Der Laan and the Plastic Number, Nexus IV: Architecture and Mathematics, eds. Kim Williamsand Jose Francisco Rodrigues, Fucecchio (Florence): Kim Williams Books, 2002.
  • Padovan, R., Dom Hans van der Laan: Modern Primitive, Architectura Natura Press, 1994. [22] Shannon, A.G., Anderson P.G. and Horadam A. F., Properties of Cordonnier, Perrin and Van der Laan numbers. International Journal of Mathematical Education in Science and Technology. 37(2006), 825-831.
  • Sahin, A., On the Q analogue of …bonacci and lucas matrices and …bonacci polynomials, Utilitas Mathematica, 100(2016), 113–125.
  • Sahin, A. and Ramírez, J. R., Determinantal and permanental representations of convolved Lucas polynomials, Appl. Math. Comput., 281(2016), 314–322.
  • Yilmaz, F. and Bozkurt D., Hessenberg matrices and the Pell and Perrin numbers, J. Number Theory. 131(8)(2011),1390–1396.
  • Yilmaz, N. and Taskara N., Matrix Sequences in terms of Padovan and Perrin Numbers, Journal of Applied Mathematics (2013), Article ID 941673.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Adem Şahin Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 66 Sayı: 1

Kaynak Göster

APA Şahin, A. (2017). On the generalized Perrin and Cordonnier matrices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 242-253. https://doi.org/10.1501/Commua1_0000000793
AMA Şahin A. On the generalized Perrin and Cordonnier matrices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2017;66(1):242-253. doi:10.1501/Commua1_0000000793
Chicago Şahin, Adem. “On the Generalized Perrin and Cordonnier Matrices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, sy. 1 (Şubat 2017): 242-53. https://doi.org/10.1501/Commua1_0000000793.
EndNote Şahin A (01 Şubat 2017) On the generalized Perrin and Cordonnier matrices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 242–253.
IEEE A. Şahin, “On the generalized Perrin and Cordonnier matrices”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 66, sy. 1, ss. 242–253, 2017, doi: 10.1501/Commua1_0000000793.
ISNAD Şahin, Adem. “On the Generalized Perrin and Cordonnier Matrices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (Şubat 2017), 242-253. https://doi.org/10.1501/Commua1_0000000793.
JAMA Şahin A. On the generalized Perrin and Cordonnier matrices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:242–253.
MLA Şahin, Adem. “On the Generalized Perrin and Cordonnier Matrices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 66, sy. 1, 2017, ss. 242-53, doi:10.1501/Commua1_0000000793.
Vancouver Şahin A. On the generalized Perrin and Cordonnier matrices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):242-53.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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