Arrangement Of Letters In Words Using Parikh Matrices - Poovanandran, Ghajendran (2019)
The Parikh matrix mapping is an ingenious generalization of the classical Parikh mapping in the aim to arithmetize words by numbers. Two words are M-equivalent if and only if they share the same Parikh matrix. The characterization of M-equivalent words remains open even for the case of the ternary alphabet. Due to the dependency of Parikh matrices on the ordering of the alphabet, the notion of strong M-equivalence was proposed as an order-independent alternative to M-equivalence. In this work, we introduce a new symmetric transformation that justifies strong M-equivalence for the ternary alphabet. We then extend certain work of §erbanuja to the context of strong equivalence and show that the number of strongly M-unambiguous prints for any alphabet is always finite.