Tridiagonal Matrices with Permanent Values Equal to k-Jacobsthal Sequence


  • Porntip Kasempin Burapha University
  • Warin Vipismakul Burapha University
  • Araya Kaewsuy Burapha University



Permanent, k-Jacobsthal Sequence, Convertible Matrix


We provide a proof that the permanents of certain tridiagonal matrices are natural numbers in a k-Jacobsthal sequence. As a consequence, such matrices are convertible.



Brualdi, R. A., Gibson, P. M., “Convex polyhedra of doubly stochastic matrices I. Applications of permanent

function”, Journal of Combinatorial Theory (A), vol.22, pp.194 – 230, 1977.

Gulec, H. H., “Permanents and Determinants of Tridiagonal Matrices with (s,t) Pell Lucus Numbers”,

International Mathematical Forum, vol.11, no.23, pp.1117 – 1122, 2017.

Jına, J., Trojovsky, P., “On Permanents of some tridiagonal matrices connected with Fibonacci numbers”,

International Journal of Pure and Applied Mathematics, vol.97, no.1, pp.79 – 87, 2014.

King, B. W., Parker, D. F., “A Fibonacci Matrix and the Permanent Function. The Fibonacci Quarterly”, vol.7,

no.5, pp.539 – 544, 1969.

Kilic, E., Tasci, D., “On the Permanents of some Tridiagonal Matrices with Applications to the Fibonacci

and Lucas numbers”, Rocky Mountain Journal of Mathematics, vol.37, no.6, pp.1953 – 1969, 2007.

Kaygisiz, K., Sahin, A., “Determinant and Permanent of Hessenberg Matrix and Fibonacci Type

Numbers”, Gen. Math. Notes, vol.9, no.2, pp.32 – 41, 2012.

Lee, G. Y. (2000). K-Lucas numbers and associated bipartite graphs. Linear Algebra and Its Applications,

vol.320, pp.51 – 61, 2000.

Minc, H., “Permanent of - circulants”, Canad. Math. Bull, vol.7, pp.253 – 263, 1964.

Yılmaz, F., Bozkurt, D, “Hessenberg matrices and the Pell and Perrin numbers”, Journal of Number Theory,

vol.131, pp.1390 – 1396, 2011.

Yilmaz, F., Bozkurt, D, “On the Fibonacci and Lucas numbers, their sums and permanents of one type

of Hessenberg Matrices”, arXiv:1302.0668 [math.NT], 2013.




How to Cite

Kasempin, P., Vipismakul, W., & Kaewsuy, A. (2020). Tridiagonal Matrices with Permanent Values Equal to k-Jacobsthal Sequence. Asian Journal of Applied Sciences, 8(5).