On Commuting Parikh q-Matrices

This paper investigates properties of words such that their Parikh q-matrices commute. For any two words u, v is an element of Sigma(k)*, the concept of q-weak ratio property between u and v is introduced. Based on this property a necessary and sufficient condition for the Parikh q-matrices of any two words over binary alphabet to commute is given. This paper also provides a special class of words over an arbitrary alphabet Sigma(k) such that their Parikh q-matrices commute.