Right circulant determinant sequences with Jacobsthal and Jacobsthal–Lucas numbers

Aldous Cesar F. Bueno
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 4, Pages 56—61
Download full paper: PDF, 161 Kb

Details

Authors and affiliations

Aldous Cesar F. Bueno
Philippine Science High School, Central Luzon Campus
Lily Hill, Clark Freeport Zone, Pampanga, Philippines

Abstract

We study two right circulant determinant sequences. The first sequence makes use of Jacobsthal numbers of the form Js+t while the other makes use of Jacobsthal–Lucas numbers of the form Ks+t, where s, t ∈ ℤ and st. We also give some open problems.

Keywords

  • Determinants sequence
  • Jacobsthal numbers
  • Jacobsthal–Lucas numbers

AMS Classification

  • 15B05

References

  1. Bahsi, M. & Solak, S.(2010) On the Circulant Matrices with Arithmetic Sequence, International Journal of Contemporary Matematical. Sciences, 5(25), 1213–1222.
  2. Bozkurt, D. (2012) On the Determinants and Inverses of Circulant Matrices with a General Number Sequence, arXiv: 1202.1068v1 [math.NA] 6 Feb 2012.
  3. Bozkurt, D. (2012) On the Determinants and Inverses of Circulant Matrices with Jacobsthal and Lucas–Jacobsthal Numbers, arXiv: 1201.6058v1 [math.NA] 29 Jan 2012.
  4. Bozkurt, D. (2012) On the Determinants and Inverses of Circulant Matrices with Pell and Pell–Lucas Numbers, arXiv: 1201.6061v1 [math.NA] 29 Jan 2012.
  5. Bueno, A.C.F. (2012) On Right Circulant Matrices with Geometric Progression, International Journal of Applied Mathematical Research, 1(4), 593–603.
  6. Bueno, A.C.F. (2012) Right Circulant Matrices with Fibonacci Sequence, International Journal of Mathematics and Scientific Computing, 2(2), 9–10.
  7. Bueno, A.C.F. (2013) Right Circulant Matrices with Jacobsthal Sequence, International Journal of Advanced Mathematical Sciences, 1(2), 87–90.
  8. Bueno, A.C.F. (2013) Generalized Right Circulant Matrices with Geometric Sequence, International Journal of Mathematics and Scientific Computing, 3(1), 17–18
  9. Bueno, A.C.F. (2014) On the Eigenvalues and the Determinant of the Right Circulant Matrices with Pell and Pell–Lucas Numbers, International Journal of Mathematics and Scientific Computing, 4(1), 19–20.
  10. Bueno, A.C.F. (2014) Right Circulant Matrices with Sum of the Terms of Two Geometric Sequences, International Journal of Mathematics and Scientific Computing, 4(2), 51–52.
  11. Civciv, H. & Turkmen, R. Notes on Norms of Circulant Matrices with Lucas Numbers, International Journal of Information and System Sciences, 4(1), 142–147.
  12. Gray, R. Toeplitz and Circulant Matrices: A Review, http://ee.stanford.edu/˜gray/toeplitz.pdf
  13. Majumdar, A.A.K. Wandering in the World of Smarandache Numbers, http://fs.gallup.unm.edu/Majumdar.pdf
  14. Nalli, A. & Sen, M. (2010) On the Norms of Circulant Matrices with Generalized Fibonacci Numbers, Selcuk Journal of Applied Mathematics, 11(1), 107–116.
  15. Shen, S. & Cen, J. (2011) On the Norms of Circulant Matrices with the (k; h)-Fibonacci and (k; h)-Lucas Numbers, International Journal of Contemporary Mathematics and Sciences, 6(19), 887–894.
  16. Yalciner, A. (2008) Spectral Norms of Some Special Circulant Matrices, International Journal of Contemporary Mathematics and Sciences, 3(35), 1733–1738.

Related papers

Cite this paper

Bueno, A. C. F. (2016). Right circulant determinant sequences with Jacobsthal and Jacobsthal–Lucas Numbers. Notes on Number Theory and Discrete Mathematics, 22(4), 56-61.

Comments are closed.