Research Article

Binomial Expansion to 1-Tridiagonal Toeplitz Determinants

Volume: 18 Number: 2 June 30, 2026
EN

Binomial Expansion to 1-Tridiagonal Toeplitz Determinants

Abstract

The determinants of 1-Tridiagonal Toeplitz matrices are computed using the Binomial Coefficient expansion considering two cases. Each expansion can be computed in parallel, which decreases algorithmic complexity and reduces the overall computation time.

Keywords

References

  1. Bergum, G.E., Hoggatt Jr, V.E., The first few terms p, Knights Tour Revisited, (1978), 285–288.
  2. Borowska, J., Łaci´nska, L., Eigenvalues of 2-tridiagonal Toeplitz matrix, Journal of Applied Mathematics and Computational Mechanics, 14(4)(2015).
  3. Borowska, J., Łaci´nska, L., Rychlewska, J., Application of difference equation to certain tridiagonal matrices, Scientific Research of the Institute of Mathematics and Computer Science, 3(11)(2012), 15–20.
  4. Gover, Michael JC, The eigenproblem of a tridiagonal 2-Toeplitz matrix, Linear Algebra and its Applications, Elsevier 197 (1994), 63–78.
  5. Lipschutz, S., Theory and Problems of Probability, McGraw-Hill, 1981.
  6. Mackey, D. S., Mackey, N., Petrovic, S., Is every matrix similar to a Toeplitz matrix?, Linear algebra and its applications, Elsevier, 297(1-3)(1999), 87–105.
  7. Trench, W.F., Some spectral properties of Hermitian Toeplitz matrices, SIAM Journal on Matrix Analysis and Applications, 15(3)(1994), 938–942.
  8. Ye, K., Lim, L-H., Every matrix is a product of Toeplitz matrices, Foundations of Computational Mathematics,Springer, 16(3)(2016), 577–598.

Details

Primary Language

English

Subjects

Numerical and Computational Mathematics (Other), Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Eugene Agyeı-kodıe This is me
United States

Publication Date

June 30, 2026

Submission Date

July 26, 2024

Acceptance Date

December 28, 2025

Published in Issue

Year 2026 Volume: 18 Number: 2

APA
Agyeı-kodıe, E., & Dogan, H. (2026). Binomial Expansion to 1-Tridiagonal Toeplitz Determinants. Turkish Journal of Mathematics and Computer Science, 18(2), 296-302. https://doi.org/10.47000/tjmcs.1523047
AMA
1.Agyeı-kodıe E, Dogan H. Binomial Expansion to 1-Tridiagonal Toeplitz Determinants. TJMCS. 2026;18(2):296-302. doi:10.47000/tjmcs.1523047
Chicago
Agyeı-kodıe, Eugene, and Hamide Dogan. 2026. “Binomial Expansion to 1-Tridiagonal Toeplitz Determinants”. Turkish Journal of Mathematics and Computer Science 18 (2): 296-302. https://doi.org/10.47000/tjmcs.1523047.
EndNote
Agyeı-kodıe E, Dogan H (June 1, 2026) Binomial Expansion to 1-Tridiagonal Toeplitz Determinants. Turkish Journal of Mathematics and Computer Science 18 2 296–302.
IEEE
[1]E. Agyeı-kodıe and H. Dogan, “Binomial Expansion to 1-Tridiagonal Toeplitz Determinants”, TJMCS, vol. 18, no. 2, pp. 296–302, June 2026, doi: 10.47000/tjmcs.1523047.
ISNAD
Agyeı-kodıe, Eugene - Dogan, Hamide. “Binomial Expansion to 1-Tridiagonal Toeplitz Determinants”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 296-302. https://doi.org/10.47000/tjmcs.1523047.
JAMA
1.Agyeı-kodıe E, Dogan H. Binomial Expansion to 1-Tridiagonal Toeplitz Determinants. TJMCS. 2026;18:296–302.
MLA
Agyeı-kodıe, Eugene, and Hamide Dogan. “Binomial Expansion to 1-Tridiagonal Toeplitz Determinants”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 296-02, doi:10.47000/tjmcs.1523047.
Vancouver
1.Eugene Agyeı-kodıe, Hamide Dogan. Binomial Expansion to 1-Tridiagonal Toeplitz Determinants. TJMCS. 2026 Jun. 1;18(2):296-302. doi:10.47000/tjmcs.1523047