Year 2024,
Volume: 14 Issue: 2, 79 - 86, 31.07.2024
Pawel Bednarz
Anetta Szynal-lıana
References
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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.,
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- [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.
Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables)
Year 2024,
Volume: 14 Issue: 2, 79 - 86, 31.07.2024
Pawel Bednarz
Anetta Szynal-lıana
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.