Determinants Containing Powers of Generalized Fibonacci Numbers

2015/12/22 by Tangboonduangjit, Aram, Thanatipanonda, Thotsaporn
#11B39 #11C20 #15B36 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.07025

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.

Related

• Determinants containing powers of polynomial sequences
• Determinants of Rising Powers of Second Order Linear Recurrence Entries by Means of the Desnanot-Jacobi Identity
• Combinatorialization of Sury and McLaughlin identities, general linear recurrences in a unified approach
• Some remarks on generalized Fibonacci and Lucas polynomials
• Some Determinantal Identities