On the Injectivity of the Parikh Matrix Mapping

Abstract

In this paper we investigate the injectivity of the Parikh matrix mapping. This research is done mainly on the binary alphabet. We identify a family of binary words, refered to as ``palindromic amiable'', such that two such words are palindromic amiable if and only if they have the same image by the Parikh matrix mapping. Some other related problems are discussed, too.