Indexed Fibonacci Arrays And Its Properties.

nth order Fibonacci word fn is defined recursively by fixing the first two initial letters, namely f0 and f1. W.H. Chaun (1993) proposed a few ways of indexing the Fibonacci words with binary sequences in order to generate the Fibonacci words. Two-dimensional Fibonacci words (or Fibonacci arrays) were first defined in the year 2000 as an infinite sequence of arrays obtained recursively by fixing the four initial letters, namely f0,0, f0,1, f1,0 and f1,1. In 2021, few results on indexed Fibonacci and indexed involutive Fibonacci words have been studied. In this paper, we extend their work to Fibonacci arrays by defining a new way of indexing and proving results based on the indexing. [ABSTRACT FROM AUTHOR]