Generalized Parikh matrices of picture array

Abstract

The theory of Parikh matrices and subword occurrences has led to extensive research in combinatorics on words. The extension of Parikh matrix of a word into picture array is an another interesting problem. Since the Parikh matrix does not say about the number of subword occurrences in the array. Therefore, in this paper we introduce the generalized Parikh matrix of a picture array which gives the number of subwords occurrences in the array. We also discuss some properties of generalized Parikh matrices.