On the Weakly Superincreasing Distributions and the Fibonacci-Hessenberg Matrices

Abstract

This paper deals with the interconnections between finite weakly superincreasing distributions, the Fibonacci sequence, and Hessenberg matrices. A frequency distribution, to be called the Fibonacci distribution, is introduced that expresses the core of the connections among these three concepts. Using a Hessenberg representation of finite weakly superincreasing distributions, it is shown that, among all such \(n\)-string frequency distributions, the Fibonacci distribution achieves the maximum expected codeword length.