On Certain Hessenberg Matrices Related with Linear Recurrences

Sibel Koparal, Neşe Ömür, Cemile D. Çolak

DOI Number
https://doi.org/10.22190/FUMI1802153K
First page
153
Last page
162

Abstract


In this paper, we present the permanents and determinants of some Hessenberg
matrices. Also, some special cases for permanents are given.


Keywords

Hessenberg matrices, permanents, determinants

Keywords


Hessenberg matrix, permanents, sequences

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References


R. A. Brualdi and P. M. Gibson: Convex Polyhedra of Doubly Stochastic MatricesI: Applications of the Permanents Function. J. Combin. Theory, Series A 22 (1977), 194– 230.

N. D. Cahill, J. R. D’Errico, D. A. Narayan and J. Y. Narayan: Fibonacci determinants. The College Math. Journal 33 (2002), no. 3, 221–225.

D. Kalman: Generalized Fibonacci numbers by matrix methods. Fibonacci Quart. 20 (1982), no.1, 73–76.

E. Kılıc¸ and D. Ta¸scı: On the permanents of some tridiagonal matrices with applications to the Fibonacci and Lucas numbers. Rocky Mountain J. Math. 37 (2007), no. 6, 203–219.

E. Kılıc¸: Tribonacci sequences with certain indices and their sums. Ars Combin. 86 (2008), 13–22.

E. Kılıc¸ and D. Tasci: On families of bipartite graphs associated with sums of Fibonacci and Lucas numbers. Ars Combin. 89 (2008), 31–40.

E. Kılıc¸ and D. Ta¸scı: Negatively subscripted Fibonacci and Lucas numbers and their complex factorizations. Ars Combin. 96 (2010), 275–288

H-C. Li: On Fibonacci-Hessenberg matrices and the Pell and Perrin numbers. Appl. Math. Comput. 218 (2012), 8353–8358.

H. Minc: Permanents of (0,1)-circulants. Canadian Math. Bulletin 7 (1964), 253–263.

J. L. Ram˜nrez: Hessenberh matrices and the generalized Fibonacci-Narayana sequence. Filomat 29 (2015), no. 7, 1557–1563.

S. Koparal, N. ¨ Om¨ur and C. D. C¸olak : Some permanents of Hessenberg matrices. Accepted in Filomat.

P. Trojovsk´ y: On determinants of tridiagonal matrices with (-1,1)-diagonal or superdiagonal in relation to Fibonacci numbers. Global Journal of Pure and Applied Mathematics 12 (2016), no. 2, 1885–1892.




DOI: https://doi.org/10.22190/FUMI1802153K

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