Injectivity of the Parikh Matrix Mappings Revisited

We deal with the notion of M-unambiguity (5) in connection with the Parikh matrix mapping introduced by Mateescu and others in (7). M-unambiguity is studied both in terms of words and matrices and several sufficient criteria for M-una mbiguity are provided in both cases, nontrivially generalizing the criteria based on the γ-property introduced by Salomaa in (15). Also, the notion of M-unambiguity with respect to a word is defined i n connection with the extended Parikh matrix morphism (16) and some of the M-unambiguity criteria are lifted from the classical setting to the extended one. This paper is an revised and extended version of (17).