Strong 2.t and Strong 3.t Transformations for Strong M-equivalence

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Parikh matrices have been extensively investigated due to their usefulness in studying subword occurrences in words. Due to the dependency of Parikh matrices on the ordering of the alphabet, strong M-equivalence was proposed as an order-independent alternative to M-equivalence in studying words possessing the same Parikh matrix. This paper introduces and studies the notions of strong 2.t and strong 3.t transformations in determining when two ternary words are strongly M-equivalent. The irreducibility of strong 2.t transformations are then scrutinized, exemplified by a structural characterization of irreducible strong 2.2 transformations. The common limitation of these transformations in characterizing strong M-equivalence is then addressed.