On strongly M-unambiguous prints and Şerbǎnuţǎ's conjecture for Parikh matrices

In the combinatorial study of words, the Parikh matrix mapping was introduced by Mateescu et al. in 2001 as a natural expansion of the classical Parikh mapping. Solving the general injectivity problem of Parikh matrices remains as one of the most sought after triumph among researchers in this area of study. In this paper, we tackle this problem by extending Şerbǎnuţǎ's work regarding prints and M-unambiguity to the context of strong M-equivalence. Consequently, we obtain results on the finiteness of strongly M-unambiguous prints for any finite alphabet. Finally, a related conjecture by Şerbǎnuţǎ is conclusively addressed.