Parikh q-Matrices and q-Ambiguous Words

Abstract

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