  The introduction of Parikh matrices by Mateescu et al. in 2001 has sparked
numerous new investigations in the theory of formal languages by various
researchers, among whom is Serbanuta. Recently, a decade-old conjecture by
Serbanuta on the M-ambiguity of words was disproved, leading to new
possibilities in the study of such words. In this paper, we investigate how
selective repeated duplications of letters in a word affect the M-ambiguity of
the resulting words. The corresponding M-ambiguity of those words are then
presented in sequences, which we term as M-ambiguity sequences. We show that
nearly all patterns of M-ambiguity sequences are attainable. Finally, by
employing certain algebraic approach and some underlying theory in integer
programming, we show that repeated periodic duplications of letters of the same
type in a word results in an M-ambiguity sequence that is eventually periodic.
