Two-dimensional picture arrays and Parikh q—matrices

Abstract

Based on the idea of “q—count” of certain subwords of a word and generalizing the notion of Parikh matrix of a word, the notion of Parikh q—matrix of a word over an ordered alphabet was introduced. On the other hand, with a two-dimensional picture array of symbols arranged in rows and columns, two kinds of upper triangular matrices, known as row and column Parikh matrices have also been introduced and investigated. Here combining these two kinds of matrices of a picture array, we introduce row/column Parikh q—matrix of an array, leading to the concept of q—ambiguity of a picture array. Results relating to q—ambiguity of picture arrays are derived in the context of these Parikh q—matrices of arrays.