Some Algebraic Aspects of Parikh q-Matrices

This paper discusses some algebraic properties of Parikh q-matrices. A new way of q-c minting of the subwords of a given word w is introduced. It has been shown that the notion of alternating Parikh q-matrices can be characterized using the q-counting polynomials. We also show that a Minor of a Parikh q-matrix is a polynomial in q with non-negative coefficients. Further this work provides an extension of the definition of partial sum circle plus to Parikh q-matrices. A characterization on words x and y such that the partial sum of their Parikh q-rnatrices is always a Parikh q-matrix is also given. We also provide some partial results for the case q = 1.