1 research outputs found
Parikh Motivated Study on Repetitions in Words
We introduce the notion of general prints of a word, which is substantialized
by certain canonical decompositions, to study repetition in words. These
associated decompositions, when applied recursively on a word, result in what
we term as core prints of the word. The length of the path to attain a core
print of a general word is scrutinized. This paper also studies the class of
square-free ternary words with respect to the Parikh matrix mapping, which is
an extension of the classical Parikh mapping. It is shown that there are only
finitely many matrix-equivalence classes of ternary words such that all words
in each class are square-free. Finally, we employ square-free morphisms to
generate infinitely many pairs of square-free ternary words that share the same
Parikh matrix.Comment: 15 pages, preprint submitte