Poovanandran, Ghajendran
(2019)
Arrangement Of Letters In Words
Using Parikh Matrices.
PhD thesis, Universiti Sains Malaysia.
Abstract
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.
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