Core words and Parikh matrices

Parikh matrices have been widely investigated due to their applicability in arithmetizing words by numbers. This paper introduces the core of a binary word, which captures the essential part of a word from the perspective of its Parikh matrix. Additionally, the stronger notion of core M-unambiguity is introduced and the characterization of core M-unambiguous binary words is obtained. Finally, a generalization of the core of a binary word and some of its interesting properties are investigated.