BINARY WORDS AND AMBIGUITY: A BRIEF SURVEY

The concept of Parikh matrix of a finite sequence w of symbols, also called a word, was developed in studying the problem of counting the number of occurrences of certain scattered subwords of the word w. Two words x and y are said to be amiable if they have the same Parikh matrix. A word is called ambiguous if it is amiable to another distinct word. In this paper we provide a brief survey on various results on ambiguity of a binary word, established in different studies in the area of research on Parikh matrix of a word.