A Characterization of the Generalized Lah Matrix

Abstract

The purpose of this note is to give the power formula of the generalized Lah matrix and show $\mathcal{L}[x,y]=\mathcal{F}\mathcal{Q}[x,y]$, where $\mathcal{F}$ is the Fibonacci matrix and $\mathcal{Q}[x,y]$ is the lower triangular matrix. From it, several combinatorial identities involving the Fibonacci numbers are obtained.