LIMITING PROBABILITY TRANSITION MATRIX OF A CONDENSED FIBONACCI TREE

Abstract

This paper discusses on the construction of condensed Fibonacci trees and present the Markov chain corresponding to the condensed Fibonacci trees. An n × n finite Markov probability transition matrix for this Markov chain is presented and it is proved that the limiting steady state probabilities are proportional to the first n Fibonacci numbers. AMS Subject Classification: 05C07, 05C38, 05C75, 05C85