Reducing the ambiguity of Parikh matrices

Abstract

The Parikh matrix mapping allows us to describe words using matrices. Although compact, this description comes with a level of ambiguity since a single matrix may describe multiple words. This work looks at how considering the Parikh matrices of various transformations of a given word can decrease that ambiguity. More specifically, for any word, we study the Parikh matrix of its Lyndon conjugate as well as that of its projection to a smaller alphabet. Our results demonstrate that ambiguity can often be reduced using these concepts, and we give conditions on when they succeed.

Counting Subwords in Circular Words and Their Parikh Matrices

“…The study of Parikh matrices in relation to conjugacy classes has been done in [8]-in particular, on the Parikh matrix of the lexicographically smallest word in a conjugacy class (i.e. Lyndon conjugate).…”