Strong (2 ⋅ t) and Strong (3 ⋅ t) Transformations for Strong M-Equivalence

Abstract

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, the notion of strong [Formula: see text]-equivalence was proposed as an order-independent alternative to [Formula: see text]-equivalence in studying words possessing the same Parikh matrix. This paper introduces and studies the notions of strong [Formula: see text] and strong [Formula: see text] transformations in determining when two ternary words are strongly [Formula: see text]-equivalent. The irreducibility of strong [Formula: see text] transformations is then scrutinized, further exemplified by a structural characterization of irreducible strong [Formula: see text] transformations. The common limitation of these transformations in characterizing strong [Formula: see text]-equivalence is then addressed.