Morphic images of binary words and Parikh matrices

Abstract

A word is a finite sequence of symbols. Parikh matrix of a word, introduced by Mateescu et al (2000), has become an effective tool in the study of certain numerical properties of words based on subwords. There have been several investigations on various properties of Parikh matrices such as M-ambiguity, M-equivalence, subword equalities and inequalities, commutativity and so on. Recently, Parikh matrices of words that are images under certain morphisms have been studied for their properties. On the other hand, Parikh matrices of words involving a certain ratio property called weak-ratio property have been investigated by Subramanian et al (2009). Here we consider two special morphisms called Fibonacci and Tribonacci morphisms and obtain properties of Parikh matrices of images of binary words under these morphisms, utilizing the notion of weak-ratio property.