This paper investigates properties of words such that their Parikh q-matrices commute. For any two words u , v ∈ ∑ 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 ∑k such that their Parikh q-matrices commute.
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