Circulants and the factorization of the Fibonacci–like numbers

Jaroslav Seibert; Pavel Trojovský

Acta Mathematica Universitatis Ostraviensis (2006)

  • Volume: 14, Issue: 1, page 63-70
  • ISSN: 1804-1388

Abstract

top
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers U n and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.

How to cite

top

Seibert, Jaroslav, and Trojovský, Pavel. "Circulants and the factorization of the Fibonacci–like numbers." Acta Mathematica Universitatis Ostraviensis 14.1 (2006): 63-70. <http://eudml.org/doc/35164>.

@article{Seibert2006,
abstract = {Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers $U_n$ and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.},
author = {Seibert, Jaroslav, Trojovský, Pavel},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Fibonacci and Lucas numbers; tridiagonal matrix; circulant; Fibonacci-like numbers; factorization},
language = {eng},
number = {1},
pages = {63-70},
publisher = {University of Ostrava},
title = {Circulants and the factorization of the Fibonacci–like numbers},
url = {http://eudml.org/doc/35164},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Seibert, Jaroslav
AU - Trojovský, Pavel
TI - Circulants and the factorization of the Fibonacci–like numbers
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2006
PB - University of Ostrava
VL - 14
IS - 1
SP - 63
EP - 70
AB - Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers $U_n$ and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
LA - eng
KW - Fibonacci and Lucas numbers; tridiagonal matrix; circulant; Fibonacci-like numbers; factorization
UR - http://eudml.org/doc/35164
ER -

References

top
  1. Fibonacci determinants, College Mathematics Journal 33.3 (2002), 221-225. (2002) 
  2. Complex factorizations of the Fibonacci and Lucas numbers, The Fibonacci Quarterly 41.1 (2003), 13-19. (2003) MR1962276
  3. Fibonacci and Lucas numbers as tridiagonal matrix determinants, The Fibonacci Quarterly 42.2 (2004), 216-221. (2004) MR2093876
  4. Tables of Integrals, Series and Products, 5th ed. San Diego, CA: Academic Press, 1979. (1979) 
  5. Elliptic functions and Lambert series in the summation of reciprocals in certain recurrence–generated sequences, The Fibonacci Quarterly 26.2 (1988), 98-114. (1988) Zbl0647.10014MR0938583

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.