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Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables)

Year 2024, Volume: 14 Issue: 2, 79 - 86, 31.07.2024
https://izlik.org/JA55YZ89SP

Abstract

In this paper, we compute paradeterminants and parapermanents of some
triangular matrices that give bihyperbolic numbers of the Fibonacci type. Using connections between the paradeterminant of triangular matrix and the lower Hessenberg
determinant, we also obtain the general term of these sequences.

References

  • [1] M. Bilgin, S. Ersoy, Algebraic properties of bihyperbolic numbers, Adv. Appl. Clifford Algebr., 30(13), 2020, 1-17.
  • [2] D. Br´od, A. Szynal-Liana, I. W loch, Bihyperbolic numbers of the Fibonacci type and their idempotent representation, Comment. Math. Univ. Carolin., 62(4), 2021, 409-416.
  • [3] D. Br´od, A. Szynal-Liana, I. W loch, On some combinatorial properties of bihyperbolic numbers of the Fibonacci type, Math. Methods Appl. Sci., 44, 2021, 4607-4615.
  • [4] J. Cockle, On a new imaginary in algebra, Lond. Edinb. Dubl. Phil. Mag., 34, 1849, 37-47.
  • [5] J. Cockle, On certain functions resembling quaternions, and on a new imaginary in algebra, Lond. Edinb. Dubl. Phil. Mag., 33, 1848, 435-439.
  • [6] J. Cockle, On impossible equations, on impossible quantities, and on tessarines, Lond. Edinb. Dubl. Phil. Mag., 37, 1850, 281-283.
  • [7] J. Cockle, On the symbols of algebra, and on the theory of tesarines, Lond. Edinb. Dubl. Phil. Mag., 34, 1849, 406-410.
  • [8] O.G. Ganyushkin, R.A. Zatorsky, I.I. Lishchinskii, On paradeterminants and parapermanents of triangular matrices, Bull. Kyiv Univ. Ser. Phys. Math., 1, 2005, 35-41.
  • [9] T. Goy, Horadam sequence through recurrent determinants of tridiagonal matrix, Kragujevac J. Math., 42(4), 2018, 527-532.
  • [10] T. Goy, R.A. Zatorsky, Infinite linear recurrence relation and superposition of linear recurrence equations, J. Integer Seq., 20(5), 2017, 1-14.
  • [11] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3.3, 1965, pp. 161-176.
  • [12] A. Szynal-Liana, I. W loch, Generalized commutative quaternions of the Fibonacci type, Bol. Soc. Mat. Mex., 28(1), 2022, https://doi.org/10.1007/s40590-021-00386-4.
  • [13] R.A. Zatorsky, Introduction to the theory of triangular matrices (tables), in: I. I. Kyrchey (Ed.), Advances in Linear Algebra Research, Nova Science Publishers, New York, 2015, 185-238.
  • 14] R.A. Zatorsky, On paradeterminants and parapermanents of triangular matrices, Mat. Stud., 17(1), 2002, 3-17.
  • [15] R.A. Zatorsky, Theory of paradeterminants and its applications, Algebra Discrete Math., 1, 2007, 108-137.
  • [16] R.A. Zatorsky, T. Goy, Parapermanents of triangular matrices and some general theorems on number sequences, J. Integer Seq., 19, 2016, 1-23.
  • [17] R.A. Zatorsky, I.I. Lishchynskyy, On connection between determinants and paradeterminants, Mat. Stud., 25, 2006, 97-102.

Year 2024, Volume: 14 Issue: 2, 79 - 86, 31.07.2024
https://izlik.org/JA55YZ89SP

Abstract

References

  • [1] M. Bilgin, S. Ersoy, Algebraic properties of bihyperbolic numbers, Adv. Appl. Clifford Algebr., 30(13), 2020, 1-17.
  • [2] D. Br´od, A. Szynal-Liana, I. W loch, Bihyperbolic numbers of the Fibonacci type and their idempotent representation, Comment. Math. Univ. Carolin., 62(4), 2021, 409-416.
  • [3] D. Br´od, A. Szynal-Liana, I. W loch, On some combinatorial properties of bihyperbolic numbers of the Fibonacci type, Math. Methods Appl. Sci., 44, 2021, 4607-4615.
  • [4] J. Cockle, On a new imaginary in algebra, Lond. Edinb. Dubl. Phil. Mag., 34, 1849, 37-47.
  • [5] J. Cockle, On certain functions resembling quaternions, and on a new imaginary in algebra, Lond. Edinb. Dubl. Phil. Mag., 33, 1848, 435-439.
  • [6] J. Cockle, On impossible equations, on impossible quantities, and on tessarines, Lond. Edinb. Dubl. Phil. Mag., 37, 1850, 281-283.
  • [7] J. Cockle, On the symbols of algebra, and on the theory of tesarines, Lond. Edinb. Dubl. Phil. Mag., 34, 1849, 406-410.
  • [8] O.G. Ganyushkin, R.A. Zatorsky, I.I. Lishchinskii, On paradeterminants and parapermanents of triangular matrices, Bull. Kyiv Univ. Ser. Phys. Math., 1, 2005, 35-41.
  • [9] T. Goy, Horadam sequence through recurrent determinants of tridiagonal matrix, Kragujevac J. Math., 42(4), 2018, 527-532.
  • [10] T. Goy, R.A. Zatorsky, Infinite linear recurrence relation and superposition of linear recurrence equations, J. Integer Seq., 20(5), 2017, 1-14.
  • [11] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3.3, 1965, pp. 161-176.
  • [12] A. Szynal-Liana, I. W loch, Generalized commutative quaternions of the Fibonacci type, Bol. Soc. Mat. Mex., 28(1), 2022, https://doi.org/10.1007/s40590-021-00386-4.
  • [13] R.A. Zatorsky, Introduction to the theory of triangular matrices (tables), in: I. I. Kyrchey (Ed.), Advances in Linear Algebra Research, Nova Science Publishers, New York, 2015, 185-238.
  • 14] R.A. Zatorsky, On paradeterminants and parapermanents of triangular matrices, Mat. Stud., 17(1), 2002, 3-17.
  • [15] R.A. Zatorsky, Theory of paradeterminants and its applications, Algebra Discrete Math., 1, 2007, 108-137.
  • [16] R.A. Zatorsky, T. Goy, Parapermanents of triangular matrices and some general theorems on number sequences, J. Integer Seq., 19, 2016, 1-23.
  • [17] R.A. Zatorsky, I.I. Lishchynskyy, On connection between determinants and paradeterminants, Mat. Stud., 25, 2006, 97-102.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematics Education, Science Education, Science and Mathematics Education (Other)
Journal Section Research Article
Authors

Pawel Bednarz This is me

Anetta Szynal-lıana

Publication Date July 31, 2024
IZ https://izlik.org/JA55YZ89SP
Published in Issue Year 2024 Volume: 14 Issue: 2

Cite

APA Bednarz, P., & Szynal-lıana, A. (2024). Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables). Azerbaijan Journal of Mathematics, 14(2), 79-86. https://izlik.org/JA55YZ89SP
AMA 1.Bednarz P, Szynal-lıana A. Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables). AZJM. 2024;14(2):79-86. https://izlik.org/JA55YZ89SP
Chicago Bednarz, Pawel, and Anetta Szynal-lıana. 2024. “Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables)”. Azerbaijan Journal of Mathematics 14 (2): 79-86. https://izlik.org/JA55YZ89SP.
EndNote Bednarz P, Szynal-lıana A (July 1, 2024) Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables). Azerbaijan Journal of Mathematics 14 2 79–86.
IEEE [1]P. Bednarz and A. Szynal-lıana, “Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables)”, AZJM, vol. 14, no. 2, pp. 79–86, July 2024, [Online]. Available: https://izlik.org/JA55YZ89SP
ISNAD Bednarz, Pawel - Szynal-lıana, Anetta. “Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables)”. Azerbaijan Journal of Mathematics 14/2 (July 1, 2024): 79-86. https://izlik.org/JA55YZ89SP.
JAMA 1.Bednarz P, Szynal-lıana A. Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables). AZJM. 2024;14:79–86.
MLA Bednarz, Pawel, and Anetta Szynal-lıana. “Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables)”. Azerbaijan Journal of Mathematics, vol. 14, no. 2, July 2024, pp. 79-86, https://izlik.org/JA55YZ89SP.
Vancouver 1.Pawel Bednarz, Anetta Szynal-lıana. Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables). AZJM [Internet]. 2024 Jul. 1;14(2):79-86. Available from: https://izlik.org/JA55YZ89SP