A New Study of Parikh Matrices Restricted to Terms

Parikh matrices as an extension of Parikh vectors are useful tools in arithmetizing words by numbers. This paper presents a further study of Parikh matrices by restricting the corresponding words to terms formed over a signature. Some M-equivalence preserving rewriting rules for such terms are introduced. A characterization of terms that are only M-equivalent to themselves is studied for binary signatures. Graphs associated to the equivalence classes of M-equivalent terms are studied with respect to graph distance. Finally, the preservation of M-equivalence under the term self-shuffle operator is studied.