Algebraic aspects of extending Parikh matrices of picture arrays

K. Janaki; R. Krishna Kumari; R. Arulprakasam

K. Janaki SAVEETHA ENGINEERING COLLEGE
R. Krishna Kumari College of Engineering and Technology,\\ SRM Institute of Science and Technology, Kattankulathur, Chennai-603203, Tamilnadu, India .\\
R. Arulprakasam College of Engineering and Technology,\\ SRM Institute of Science and Technology, Kattankulathur, Chennai-603203, Tamilnadu, India

Abstract

As a natural extension of the Parikh matrix of a picture array induced by an alphabet, this paper investigates the concept of extending the Parikh matrix of a picture array induced by a word with some elementary properties. We also examine the relationship between an extending Parikh matrix and a Parikh matrix. In addition, we analyze u?ambiguity of picture arrays and discuss its properties. Furthermore, we extend Parikh friendly permutation to picture arrays in the context of Parikh matrices. With the aid of extending Parikh matrix, we analyze the properties of power of the picture arrays.