On M-unambiguity of Parikh matrices
Indonesian Journal of Combinatorics
https://doi.org/10.19184/IJC.2020.4.1.1Abstract
The Parikh matrix mapping was introduced by Mateescu et al. in 2001 as a canonical generalization of the classical Parikh mapping. The injectivity problem of Parikh matrices, even for ternary case, has withstanded numerous attempts over a decade by various researchers, among whom is Serbanuta. Certain M-ambiguous words are crucial in Serbanuta's findings about the number of M-unambiguous prints. We will show that these words are in fact strongly M-ambiguous, thus suggesting a possible extension of Serbanuta’s work to the context of strong M-equivalence. In addition, initial results pertaining to a related conjecture by Serbanuta will be presented.
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- Every word w such that pr(w ) = w is M-unambiguous.
- M-unambiguous, consecutive letters in w must be adjacent in Σ. Hence, the conclusion holds easily if w has length at most two. Assume |w| ≥ 3. If xyx is a factor of w where the letters x and y are adjacent in Σ, then because xyyx is M-equivalent to References
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