Parikh Matrices and Strong M-Equivalence

Wen Chean Teh

Published 2015-01-29Version 1

Parikh matrices have been a powerful tool in arithmetizing words by numerical quantities. However, the dependence on the ordering of the alphabet is inherited by Parikh matrices. Strong M-equivalence is proposed as a canonical alternative to M-equivalence to get rid of this undesirable property. This new combinatorial property proves to be natural and interesting on its own. Some characterization results for $M$-equivalence as well as strong $M$-equivalence are obtained. Finally, the opposite notion of weak $M$-equivalence will be presented.