Publication: Arrangement Of Letters In Words Using Parikh Matrices
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Date
2019-04
Authors
Poovanandran, Ghajendran
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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.