Determinants Containing Powers of Generalized Fibonacci Numbers
Combinatorics
2016-08-02 v2
Abstract
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These studies have led us to discover a fundamental identity of determinant involving powers of linear polynomials. Finally, we discuss the determinants of matrices whose entries are products of the generalized Fibonacci numbers.
Cite
@article{arxiv.1512.07025,
title = {Determinants Containing Powers of Generalized Fibonacci Numbers},
author = {Aram Tangboonduangjit and Thotsaporn Thanatipanonda},
journal= {arXiv preprint arXiv:1512.07025},
year = {2016}
}