On M-unambiguity of Parikh matrices

Wen Chean Teh (School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Malaysia)

Indonesian Journal of Combinatorics
Vol 4, No 1 (2020)

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.