Parikh q-Matrices and q-Ambiguous Words

The Parikh matrix mapping plays an important role in the study of words through numerical properties. The Parikh q-matrix mapping, introduced by Egecioglu and Ibarra (2004) as an extension of the Parikh matrix mapping, maps words to matrices with polynomial entries in q. A word w over an ordered alphabet ς is said to be q-ambiguous if there exists another word v over ς such that both the words have same Parikh q-matrix. Here we derive several properties of q-ambiguous words, in particular, for a binary alphabet.